Complex Kleinian Groups

This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincare, Picard and many others. K

The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, the last few years having seen the resolution of many longstanding conjectures. This volume contains important expositions and original work by some of the main contributors on topics such as topology and geometry of 3-manifolds, curve complexes, classical Ahlfors-Bers theory, computer explorations and projective structures. Researchers in these and related areas will find much of interest here.

Weyl groups are particular cases of complex reflection groups, i.e. finite subgroups of GLr(C) generated by (pseudo)reflections. These are groups whose polynomial ring of invariants is a polynomial al

The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, with many old problems and conjectures close to resolution. This volume, proceedings of the Warwick workshop in September 2001, contains expositions of many of these breakthroughs including Minsky's lectures on the first half of the proof of the Ending Lamination Conjecture, the Bers Density Conjecture by Brock and Bromberg, the Tameness Conjecture by Kleineidam and Souto, the state of the art in cone manifolds by Hodgson and Kerckhoff, and the counter example to Thurston's K=2 conjecture by Epstein, Marden and Markovic. It also contains Jørgensen's famous paper 'On pairs of once punctured tori' in print for the first time. The excellent collection of papers here will appeal to graduate students, who will find much here to inspire them, and established researchers who will find this valuable as a snapshot of current research.

What are groups? How do they behave? Arrow, McGrath, and Berdahl answer these questions by developing a general theory of small groups as complex systems. Basing their theory on concepts distilled fr

Violent conflict brings together two seemingly disparate groups: humanitarians and soldiers. This mixes and convolutes agendas, blurring lines that are often perceived to be sacrosanct. Delving deepl

This volume consists of one expository paper and two research papers: T Hirai, A Hora and E Hirai, Introductory expositions on projective representations of groups (referred as [E]) T Hirai, E

During the past decade there has been a great increase in the use of protective groups, especially in the synthesis of large and complex organic molecules. Perhaps the greatest activity has been in th

This book is a compilation of the entire research work on the topic of Complex Binary Number System (CBNS) carried out by the author as the principal investigator and members of his research groups at

Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploratio

Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploratio

Hyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex anal

"The book is largely self-contained...There is a nice introduction to symplectic geometry and a charming exposition of equivariant K-theory. Both are enlivened by examples related to groups...An attra

A complex reflection is a linear transformation which fixes each point in a hyperplane. Intuitively, it resembles the transformation an image undergoes when it is viewed through a kaleidoscope, or arrangement of mirrors. This book gives a complete classification of all groups of transformations of n-dimensional complex space which are generated by complex reflections, using the method of line systems. In particular: irreducible groups are studied in detail, and are identified with finite linear groups; reflection subgroups of reflection groups are completely classified; the theory of eigenspaces of elements of reflection groups is discussed fully; an appendix outlines links to representation theory, topology and mathematical physics. Containing over 100 exercises ranging in difficulty from elementary to research level, this book is ideal for honours and graduate students, or for researchers in algebra, topology and mathematical physics.

Insolvency within multinational enterprise groups (MEGs) raises complex issues due to the foreign elements of the case and the multiplicity of debtors. The key problem is deciding to what extent and i

This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex ge

In 1970 Bernd Fischer proved his beautiful theorem classifying the almost simple groups generated by 3-transpositions, and in the process discovered three new sporadic groups, now known as the Fischer groups. Since then, the theory of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place. Fischer's result, while important and deep (covering a number of complex examples), can be understood by any student with some knowledge of elementary group theory and finite geometry. Thus Part I has minimal prerequisites and could be used as a text for an intermediate level graduate course. Parts II and III are aimed at specialists in finite groups and are a step in the author's program to supply a strong foundation for the theory of sporadic groups.

Berkovich (retired, mathematics, U. of Haifa, Israel) continues his exposition of the theory of finite prime power order groups (p-groups), moving on to more complex materials and adding material on 2

This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex ge

This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory. The first part of the book is quite elementary, and leads up to the basic rigidity criteria for the realisation of groups as Galois groups. The second part presents more advanced topics, such as braid group action and moduli spaces for covers of the Riemann sphere, GAR- and GAL- realizations, and patching over complete valued fields. Graduate students and mathematicians from other areas (especially group theory) will find this an excellent introduction to a fascinating field.

This classic introduction to human variation has been updated to include the issues and controversies facing the contemporary study of diversity. Covers the adaptation of complex traits; how the rac

Can we understand important social issues by studying individual personalities and decisions? Or are societies somehow more than the people in them? Sociologists have long believed that psychology can't explain what happens when people work together in complex modern societies. In contrast, most psychologists and economists believe that if we have an accurate theory of how individuals make choices and act on them, we can explain pretty much everything about social life. Social Emergence takes a new approach to these longstanding questions. Sawyer argues that societies are complex dynamical systems, and that the best way to resolve these debates is by developing the concept of emergence, focusing on multiple levels of analysis - individuals, interactions, and groups - and with a dynamic focus on how social group phenomena emerge from communication processes among individual members. This book makes a unique contribution not only to complex systems research but also to social theory.

This book deals with automorphism groups of compact Riemann surfaces, of genus at least two, viewed as factor groups of Fuchsian groups. The author uses modern methods from computational group theory and representation theory, providing classifications of all automorphism groups up to genus 48. The book also classifies the ordinary characters for several groups, arising from the action of automorphisms on the space of holomorphic abelian differentials of a compact Reimann surface. This book is suitable for graduate students and researchers in group theory, representation theory, complex analysis and computer algebra.

Intensive excavations in settlement areas within greater Tikal generated far more than an understanding of the complex gradations of social classes at this lowland Maya site. Identification of a speci

This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory. The first part of the book is quite elementary, and leads up to the basic rigidity criteria for the realisation of groups as Galois groups. The second part presents more advanced topics, such as braid group action and moduli spaces for covers of the Riemann sphere, GAR- and GAL- realizations, and patching over complete valued fields. Graduate students and mathematicians from other areas (especially group theory) will find this an excellent introduction to a fascinating field.

This book constitutes the proceedings of a conference held at the University of Birmingham to mark the retirement of Professor A. M. Macbeath. The papers represent up-to-date work on a broad spectrum of topics in the theory of discrete group actions, ranging from presentations of finite groups through the detailed study of Fuchsian and crystallographic groups, to applications of group actions in low dimensional topology, complex analysis, algebraic geometry and number theory. For those wishing to pursue research in these areas, this volume offers a valuable summary of contemporary thought and a source of fresh geometric insights.

Now available in paperback--the standard introduction to the theory of simple groups of Lie type. In 1955, Chevalley showed how to construct analogues of the complex simple Lie groups over arbitrary f

This book follows the same successful approach as Dr Burn's previous book on number theory. It consists of a carefully constructed sequence of questions which will enable the reader, through his or her own participation, to generate all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationship to three-dimensional isometries are covered, and the climax of the book is a study of crystallographic groups, with a complete analysis of these groups in two dimensions.

Elliptic functions and Riemann surfaces played an important role in nineteenth-century mathematics. At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many areas of mathematical research from group theory and number theory to topology and differential equations. In this book the authors give elementary accounts of many aspects of classical complex function theory including Möbius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. A distinctive feature of their presentation is the way in which they have incorporated into the text many interesting topics from other branches of mathematics. This book is based on lectures given to advanced undergraduates and is well-suited as a textbook for a second course in complex function theory. Professionals will also find it valuable as a straightforward introduction to a subject which is finding widespread applic

Underlying Julia Kristeva’s Nations Without Nationalism is the idea that otherness—whether it be ethnic, religious, social, or political—needs to be understood and accepted in order to guarantee social harmony. This book is an impassioned plea for tolerance and for commonality, aimed at a world brimming over with racism and xenophobia. Responding to the rise of neo-Nazi groups in Germany and Eastern Europe and the popularity of the National Front in France, Kristeva turns to the origins of the nation-state to illustrate the problematic nature of nationalism and its complex configurations in subsequent centuries. For Kristeva, the key to commonality can be found in Montesquieu’s esprit general—his notion of the social body as a guaranteed hierarchy of private rights.Nations Without Nationalism also contains Kristeva’s thoughts on Harlem Desir, the founder of the antiracist organization SOS Racisme; the links between psychoanalysis and nationalism; the historical nature of French nationa

● 依照自然界和社會生活中的事物分類，“近取諸身，遠取諸物”，共劃分為九個主題。● 解釋古文字形，追溯字本義和引申義，以幫助讀者更好地理解現代漢語中的字詞。● 收入常用漢字約2500個，依照共同形符、共同聲符或字形相近等原則組成字組，以簡馭繁，以類相從。● 收入常用詞約4000個， 按照其中體現的字義排布於對應的字下面，大多數詞配有精美插圖，生動活潑地詮釋詞義，妙趣橫生。● The dictionary features 9 thematic units categorized by what’s common in nature and daily life, progressing from what is near at hand to understand oneself, to more distant things to comprehend the world.● It explains ancient forms of characters to reveal their original meanings and extended meanings, facilitating a better understanding of modern Chinese.● About 2500 of the most frequently used characters are organized into groups based on the same radicals, phonetic components, or similar forms. Simplify the complex and follow the similar.● About 4000 of the most frequently used words are listed under the corresponding characters, with most of them illustrated, making the learning process enjoyable.

An indispensable resource for organizing solidarity in diverse communities. On the heels of recent revelations of past and ongoing injustices, reconciliation and solidarity between Indigenous and non-Indigenous people are even more urgent. But it is a complex endeavor. In The Solidarity Encounter, Carol Lynne D'Arcangelis takes readers into the fraught terrain of solidarity organizing, bringing together insights from both interviews with activists and current scholarship. Multi-issue coalitions such as Idle No More, #NoDAPL, MMIWG2SQ, Black Lives Matter, and Fridays for Future all depend on the collaboration of diverse communities, even as tensions emerge in the encounter between groups of unequal power. The Solidarity Encounter offers strategies for respecting boundaries, providing a constructive framework for non-colonizing solidarity that can be applied in many contexts.

Ancient Gordion has long been recognized as a key Iron Age site for Anatolia and the eastern Mediterranean. Archaeological research has revealed much about its sequence of occupation. However, as yet no study has explored the underlying drivers of political and economic change at this site. This volume presents an overview of the political and economic histories supporting emergent elites and how they constructed power at Gordion during the Iron Age (1200-300 BCE). Based on geochemical and typological analysis of nearly 2000 Late Bronze Age to Hellenistic ceramic samples, the volume contextualizes this primary dataset through the lens of ceramic production, consumption, exchange and emulation. Synthesizing site data sets, the volume more broadly contributes to our understanding of the pivotal role of groups and their economic, social, and ritual practices in the creation of complex societies.

Ancient Gordion has long been recognized as a key Iron Age site for Anatolia and the eastern Mediterranean. Archaeological research has revealed much about its sequence of occupation. However, as yet no study has explored the underlying drivers of political and economic change at this site. This volume presents an overview of the political and economic histories supporting emergent elites and how they constructed power at Gordion during the Iron Age (1200-300 BCE). Based on geochemical and typological analysis of nearly 2000 Late Bronze Age to Hellenistic ceramic samples, the volume contextualizes this primary dataset through the lens of ceramic production, consumption, exchange and emulation. Synthesizing site data sets, the volume more broadly contributes to our understanding of the pivotal role of groups and their economic, social, and ritual practices in the creation of complex societies.

Florence Thépot provides the first systematic account of the interaction between competition law and corporate governance. She challenges the 'black box' conception of the firm- or 'undertaking' - in competition law, as applied to increasingly complex corporate relations. The book opens the 'black box' of the firm to understand the internal drivers of collusive behaviour, and proposes a unified approach to cartel enforcement, based on the agency theory. It explores key issues including corporate compliance programmes, the attribution of liability in corporate groups, and structural links between competitors, and should be read by anyone interested in how the evolution of the corporate landscape impacts competition law.

This collection of cutting-edge scholarship examines the law and policy of financial regulation using a combination of conceptual analysis and strong empirical research. The book's authors range from global leaders to rising stars in the field, all of whom shed light on complex questions of financial sector regulation theory and practice in key economies ranging from the EU to China. Key topics include the role of law in constituting financial markets, the efficiency of markets, the role of interest groups in shaping financial regulation, the interdependence and interactions of international financial regulation with international trade and monetary regimes, and problems of regulation in state capitalism economies. This exciting volume opens the road for further enrichment of the academic and policy-making dialogue on financial regulation and regulatory practice, and reflects new trends in legal and social-science scholarship.

Describes and illustrates the full range of Dutch resistance groups and German and collaborationist counter-resistance groups during the Nazi occupation in 1940-45.The Nazi occupation of the Netherlands was a complex, varied and bloody affair. Well- documented is the initial capture by the Gestapo of a secret Dutch Special Operations Executive radio-operator who thereafter lured several parachuted agents to their deaths, but, the actual scope and complexity of the occupation was much greater than this. Large-scale civil resistance against the occupation began as early as February 1941, and 1943 saw assassinations, reprisals, and the development of various resistance groups – the LKP National Assault Teams and some “wild” armed groups: the left wing RzV and the conservative OD. In addition, several overlapping Dutch organizations amalgamated in September 1944 into the NBS: “Netherlands Interior Forces.” In return, the Germans created the collaborationist Landwacht security force. From t

Concealed within the walls of settlements along the Green-Line, the border between Israel and the occupied West-Bank, is a complex history of territoriality, privatisation and multifaceted class dynamics. Since the late 1970s, the state aimed to expand the heavily populated coastal area eastwards into the occupied Palestinian territories, granting favoured groups of individuals, developers and entrepreneurs the ability to influence the formation of built space as a means to continuously develop and settle national frontiers. As these settlements developed, they became a physical manifestation of the relationship between the political interest to control space and the ability to form it. Telling a socio-political and economic story from an architectural and urban history perspective, Gabriel Schwake demonstrates how this production of space can be seen not only as a cultural phenomenon, but also as one that is deeply entangled with geopolitical agendas.

This title provides accountants and auditors with easy to follow and well structured guidance on the preparation of group accounts in line with UK GAAP. Group accounts must be prepared, by law, for medium-sized and large groups. Listed companies are required to prepare their accounts in line with International Financial Reporting Standards but larger unlisted companies can prepare their statements using UK GAAP.Groups are very common in the UK and are likely to become even more common when corporation tax rates increase in the future as there are various tax advantages to operating under a group structure. Group structures can vary (e.g. horizontal, vertical, hybrid, D-shaped|) and preparing financial accurate financial statements can be complex as a result.While there is a lot of guidance on producing accounts under IFRS, there is every little in evidence dealing with the UK GAAP rules. This title addresses this gap. The commentary identifies the differences between IFRS and UK GAAP i