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Obstructions for constructing equivariant fibrations

Aslı Güçlükan İlhan

Algebraic & Geometric Topology 12 (2012) 1313–1330

Let G be a finite group and 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 and let = {FH}H be a compatible family of H–spaces. A G–fibration over B with the fiber type = {FH}H is a G–equivariant fibration p: E B where p1(b) is Gb–homotopy equivalent to FGb for each b B. In this paper, we develop an obstruction theory for constructing G–fibrations with the fiber type over a given G–CW–complex B. Constructing G–fibrations with a prescribed fiber type is an important step in the construction of free G–actions on finite CW–complexes which are homotopy equivalent to a product of spheres.

equivariant fibration, Bredon cohomology, obstruction theory, group action
Mathematical Subject Classification 2010
Primary: 57S25
Secondary: 55R91
Received: 21 October 2011
Revised: 13 March 2012
Accepted: 29 March 2012
Published: 15 June 2012
Aslı Güçlükan İlhan
Department of Mathematics
Bilkent University
Ankara 06800