Equivariant Ordinary Homology and Cohomology

✍ Scribed by Steven R. Costenoble, Stefan Waner (auth.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 308
• Series: Lecture Notes in Mathematics 2178
• Edition: 1
• Category: Library

✦ Synopsis

Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries. The discussion is motivated by reference to a list of instructive “toy” examples and calculations in what is a relatively unexplored field. The authors also provide a reading path for the first-time reader less interested in working through sophisticated machinery but still desiring a rigorous understanding of the main concepts. The subject’s classical counterparts, ordinary homology and cohomology, dating back to the work of Henri Poincaré in topology, are calculational and theoretical tools which are important in many parts of mathematics and theoretical physics, particularly in the study of manifolds. Similarly powerful tools have been lacking, however, in the context of equivariant topology. Aimed at advanced graduate students and researchers in algebraic topology and related fields, the book assumes knowledge of basic algebraic topology and group actions.

✦ Table of Contents

Front Matter....Pages i-xiv
RO(G)-Graded Ordinary Homology and Cohomology....Pages 1-154
Parametrized Homotopy Theory and Fundamental Groupoids....Pages 155-202
(RO(\Pi B)) -Graded Ordinary Homology and Cohomology....Pages 203-281
Back Matter....Pages 283-296

✦ Subjects

Algebraic Topology;Manifolds and Cell Complexes (incl. Diff.Topology);Category Theory, Homological Algebra;Topological Groups, Lie Groups