Principal Bundles ― The Classical Case

This introductory graduate level text provides a relatively quick path to a special topic in classical differential geometry: principal bundles, whose properties, including connections and their curvature, are described in some detail. The topic of principal bundles in differential geometry has become classic, even standard, material in the modern graduate mathematics curriculum, which has been treated in various texts.

The unique approach taken in this text presents the material in a way that is intuitive for both students of mathematics and of physics. From a physics standpoint, the topic of principle bundles is essentially gauge theory expressed in geometric language. This book presents important, modern geometric ideas in a form readily accessible to students and researchers in both the physics and mathematics communities, providing each with an understanding and appreciation of the language and ideas of the other.