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Group Actions on Algebraic Cell Complexes

P. H. Kropholler and C. T. C. Wall

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We establish an algebraic version of the classical result that a $G$-map $f$ between $G$-complexes which restricts to a homotopy equivalence $f^H$ on $H$-fixed sets for all subgroups $H$ of $G$ is a $G$-homotopy equivalence. This is used to give an alternative proof of a theorem of Bouc. We also include a number of illustrations and applications.

Article information

Publ. Mat., Volume 55, Number 1 (2011), 3-18.

First available in Project Euclid: 25 February 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57Q05: General topology of complexes 20J05: Homological methods in group theory

Cell complex group action equivariant homotopy


Kropholler, P. H.; Wall, C. T. C. Group Actions on Algebraic Cell Complexes. Publ. Mat. 55 (2011), no. 1, 3--18.

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