Metric Embeddings ─ Bilipschitz and Coarse Embeddings into Banach Spaces

Embeddings of discrete metric spaces into Banach spaces has become an important tool in computer science and topology, says Ostovskii (mathematics and computer science, St. John's U., New York City), and he presents some of the most important techniques and results. His topics include how the embeddability of locally finite metric spaces into Banach space is finitely determined, constructions of embeddings, Banach spaces that do not admit uniformly coarse embeddings of expanders, applying Markov chains to embeddability problems, and Lipschitz free spaces. Each chapter contains exercises, notes and remarks on the chapter, and hints to the exercises. The volume concludes with a section of open problems. Annotation c2013 Book News, Inc., Portland, OR (booknews.com)

Mikhail I. Ostrovskii, St. John's University, Queens,USA.