Description
Book SynopsisIntroduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. This book begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory.
Table of ContentsIntroduction Equivariant cellular and homology theory Postnikov systems, localization, and completion Equivariant rational homotopy theory Smith theory Categorical constructions; equivariant applications The homotopy theory of diagrams Equivariant bundle theory and classifying spaces The Sullivan conjecture An introduction to equivariant stable homotopy $G$-CW$(V)$ complexes and $RO(G)$-graded cohomology The equivariant Hurewicz and suspension theorems The equivariant stable homotopy category $RO(G)$-graded homology and cohomology theories An introduction to equivariant $K$-theory An introduction to equivariant cobordism Spectra and $G$-spectra; change of groups; duality The Burnside ring Transfer maps in equivariant bundle theory Stable homotopy and Mackey functors The Segal conjecture Generalized Tate cohomology Twisted half-smash products and function spectra Brave new algebra Brave new equivariant foundations Brave new equivariant algebra Localization and completion in complex bordism A completion theorem in complex cobordism Calculations in complex equivariant bordism Bibliography Index.
