Transitivity is not a (big) restriction on homotopy types
Combinatorics
2014-09-18 v1
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.
Cite
@article{arxiv.1409.4966,
title = {Transitivity is not a (big) restriction on homotopy types},
author = {Michal Adamaszek},
journal= {arXiv preprint arXiv:1409.4966},
year = {2014}
}