Constructing homologically trivial actions on products of spheres

Details Constructing homologically trivial actions on products of spheres Constructing homologically trivial actions on products of spheres

2012-03-27

arxiv.org/abs/1203.5882v1

Mathematics

Algebraic Topology

Scientific paper

We prove that if a finite group $G$ has a representation with fixity $f$,
then it acts freely and homologically trivially on a finite CW-complex homotopy
equivalent to a product of $f+1$ spheres. This shows, in particular, that every
finite group acts freely and homologically trivially on some finite CW-complex
homotopy equivalent to a product of spheres.

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