P.L. Homeomorphic Manifolds are Equivalent by Elementary Shellings

AbstractShellability of simplicial complexes has been a powerful concept in polyhedral theory, in p.l. topology and recently in connection with Cohen-Macaulay rings and toric varieties. It is well known that all 2-spheres and all boundary complexes of convex polytopes are shellable, but the analogous theorem fails for general simplicial balls and spheres. In this paper we study transformations of simplicial p.l. manifolds by elementary boundary operations (shellings and inverse shellings). As the main result we shall show that a simplicial p.l. manifold M can be transformed to any other simplical p.l. manifold M homeomorphic to M using these elementary operations. The tools we need and related results are summarized. In the last part we study generalized sheltings of totally strongly connected simplicial complexes and the effects on the face numbers of the complex