A counterexample to Wegner's conjecture on good covers
Combinatorics
2010-08-12 v1
Abstract
In 1975 Wegner conjectured that the nerve of every finite good cover in R^d is d-collapsible. We disprove this conjecture. A good cover is a collection of open sets in R^d such that the intersection of every subcollection is either empty or homeomorphic to an open d-ball. A simplicial complex is d-collapsible if it can be reduced to an empty complex by repeatedly removing a face of dimension at most d-1 which is contained in a unique maximal face.
Keywords
Cite
@article{arxiv.1008.1895,
title = {A counterexample to Wegner's conjecture on good covers},
author = {Martin Tancer},
journal= {arXiv preprint arXiv:1008.1895},
year = {2010}
}
Comments
8 pages, 3 figures; recommended to print in color