Obstructions for constructing equivariant fibrations

Güçlükan İlhan, Aslı

doi:10.2140/agt.2012.12.1313

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Obstructions for constructing equivariant fibrations

Aslı Güçlükan İlhan

Algebraic & Geometric Topology 12 (2012) 1313–1330

DOI: 10.2140/agt.2012.12.1313

Abstract

Let $G$ be a finite group and $ℋ$ be a family of subgroups of $G$ which is closed under conjugation and taking subgroups. Let $B$ be a $G$ –CW–complex whose isotropy subgroups are in $ℋ$ and let $ℱ = {F_{H}}_{H \in ℋ}$ be a compatible family of $H$ –spaces. A $G$ –fibration over $B$ with the fiber type $ℱ = {F_{H}}_{H \in ℋ}$ is a $G$ –equivariant fibration $p : E \to B$ where $p^{- 1} (b)$ is $G_{b}$ –homotopy equivalent to $F_{G_{b}}$ for each $b \in B$ . In this paper, we develop an obstruction theory for constructing $G$ –fibrations with the fiber type $ℱ$ over a given $G$ –CW–complex $B$ . Constructing $G$ –fibrations with a prescribed fiber type $ℱ$ is an important step in the construction of free $G$ –actions on finite CW–complexes which are homotopy equivalent to a product of spheres.

Keywords

equivariant fibration, Bredon cohomology, obstruction theory, group action

Mathematical Subject Classification 2010

Primary: 57S25

Secondary: 55R91

References

Publication

Received: 21 October 2011

Revised: 13 March 2012

Accepted: 29 March 2012

Published: 15 June 2012

Authors

Aslı Güçlükan İlhan
Department of Mathematics Bilkent University Ankara 06800 Turkey
http://www.fen.bilkent.edu.tr/~guclukan

Volume 12, issue 3 (2012)