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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747

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 = {FH}H in H be a compatible family of H–spaces. A G–fibration over B with the fiber type F = {FH}H in H is a G–equivariant fibration p: E B where p1(b) is Gb–homotopy equivalent to FGb 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

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