This book provides a striking synthesis of the standard theory of
connections in principal bundles and the Lie theory of Lie
groupoids. The concept of Lie groupoid is a little-known
formulation of the concept of principal bundle and corresponding to
the Lie algebra of a Lie group is the concept of Lie algebroid: in
principal bundle terms this is the Atiyah sequence. The author's
viewpoint is that certain deep problems in connection theory are
best addressed by groupoid and Lie algebroid methods. After
preliminary chapters on topological groupoids, the author gives the
first unified and detailed account of the theory of Lie groupoids
and Lie algebroids. He then applies this theory to the cohomology
of Lie algebroids, re-interpreting connection theory in
cohomological terms, and giving criteria for the existence of (not
necessarily Riemannian) connections with prescribed curvature form.
This material, presented in the last two chapters, is work of the
author published here for the first time. This book will be of
interest to differential geometers working in general connection
theory and to researchers in theoretical physics and other fields
who make use of connection theory.
|Country of origin:
||London Mathematical Society Lecture Note Series
||228 x 152 x 21mm (L x W x T)
||Paperback - Trade
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