Betti numbers of complexes with highly Connected links
Combinatorics
2017-03-17 v1
Abstract
Let X be a k-dimensional simplicial complex such that the (k-j-2)-dimensional homology of the links of all j-dimensional simplices in X vanishes. An upper bound is given on the (k-1)-th Betti number of X. Examples based on sum complexes show that this bound is asymptotically sharp for all fixed j<k.
Cite
@article{arxiv.1703.05562,
title = {Betti numbers of complexes with highly Connected links},
author = {Amir Abu-Fraiha and Roy Meshulam},
journal= {arXiv preprint arXiv:1703.05562},
year = {2017}
}
Comments
13 pages, 3 figures