Publikace na Matematicko-fyzikální fakulta |
2012
Abstrakt
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.