Invariant groups on equivalent crystallizations (Q1263844)

For each n-crystallization H, \(n\geq 2\), two sequences of groups \(\xi^ n_ k(H)\), \({\dot \xi}{}^ n_ k(H)\), \(0\leq k\leq n-1\), are associated. These groups are proved to be invariant under the crystallization waves of Ferri and Gagliardi (which yield a combinatorial counterpart for homeomorphisms). It follows that the groups are topological invariants for closed PL n-manifolds. From the second term on each group is a quotient of its predecessor in each sequence; also each \({\dot \xi}{}^ n_ k(H)\) is a quotient of \(\xi^ n_ k(H)\). The smallest group \(\xi^ n_{n-1}(H)\) is the fundamental group of the associated manifold \(| K(H)|\).