Transitivity is Not a (Big) Restriction on Homotopy Types

Adamaszek, Michal

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Transitivity is Not a (Big) Restriction on Homotopy Types

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Adamaszek, Michal
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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arXiv:1409.4966.pdf
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Adamaszek, M. (2014). Transitivity is Not a (Big) Restriction on Homotopy Types. Retrieved from http://arxiv.org/abs/1409.4966.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0024-4478-C

Abstract

For every simplicial complex K there exists a vertex-transitive simplicial complex homotopy equivalent to a wedge of copies of K with some copies of the circle. It follows that every simplicial complex can occur as a homotopy wedge summand in some vertex-transitive complex. One can even demand that the vertex-transitive complex is the clique complex of a Cayley graph or that it is facet-transitive.