A structure theorem for homology 4-manifolds with g2 ≤ 5

Abstract

Numerous structural findings of homology manifolds have been derived in various ways in relation to g2-values. The homology 4-manifolds with g2≤5 are characterized combinatorially in this article. It is well-known that all homology 4-manifolds for g2≤2 are polytopal spheres. We demonstrate that homology 4-manifolds with g2≤5 are triangulated spheres and are derived from triangulated 4-spheres with g2≤2 by a series of connected sum, bistellar 1- and 2-moves, edge contraction, edge expansion, and edge flipping operations. We establish that the above inequality is optimally attainable, i.e., it cannot be extended to g2=6.