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      Obstructions for constructing equivariant fibrations

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      Author(s)
      Ilhan, A.G.
      Date
      2012
      Source Title
      Algebraic and Geometric Topology
      Print ISSN
      14722747
      Volume
      12
      Issue
      3
      Pages
      1313 - 1330
      Language
      English
      Type
      Article
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      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 e{open}H be a compatible family of H -spaces. A G -fibration over B with the fiber type F = {F H} H e{open}H is a G -equivariant fibration p: E → B where p -1(b) is G b -homotopy equivalent to F Gb for each b e{open} 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
      Bredon cohomology
      Equivariant fibration
      Group action
      Obstruction theory
      Permalink
      http://hdl.handle.net/11693/21395
      Published Version (Please cite this version)
      10.2140/agt.2012.12.1313
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      • Department of Mathematics 653
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