Betti numbers of complexes with highly connected links

摘要

Let Delta((k))(n-1) denote the k-dimensional skeleton of the (n - 1)- simplex and consider a complex Delta((k-1))(n-1) subset of X subset of Delta((k))(n-1). Let K be a field and let 0 <= l < k. It is shown that if <(H)over tilde>(k-l-2)(lk(X,tau);K) = 0 for all l-dimensional faces tau of X then