From wall spaces to CAT(0) cube complexes

Details From wall spaces to CAT(0) cube complexes From wall spaces to CAT(0) cube complexes

2003-09-02

arxiv.org/abs/math/0309036v3

Mathematics

Geometric Topology

Updated to submitted version

Scientific paper

We explain how to adapt a construction of M. Sageev's to construct a proper
action on a CAT(0) cube complex starting from a proper action on a wall space,
and use this to deduce that if G is a group containing an amenable subgroup H
of super-polynomial growth and G acts properly on a space with walls then there
are arbitrarily large families of walls in the wall space which pairwise cross.

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