Triangulated n-manifolds are determined by their \([n/2]+1\)-skeletons (Q760950)

The author proves, by very simple combinatorial and homological arguments, that if \(M^ m\) and \(N^ n\) are distinct triangulated closed topological manifolds (or homology manifolds with \(m=n)\), then they have distinct k-skeletons for \(k>\max \{m,n\}\) (and, as is readily seen, ''distinct'' can be replaced by ''nonisomorphic'' in this statement).