Betti numbers of complexes with highly Connected links
Amir Abu-Fraiha, Roy Meshulam · arXiv (Cornell University) · 2017
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