A characterization of homology manifolds with g₂≤ 2

2016/07/19 by Zheng, Hailun · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.05757

Abstract

We characterize homology manifolds with g₂≤ 2. Specifically, using retriangulations of simplicial complexes, we give a short proof of Nevo and Novinsky's result on the characterization of homology (d-1)-spheres with g₂=1 for d≥ 5 and extend it to the class of normal pseudomanifolds. We proceed to prove that every prime homology manifold with g₂=2 is obtained by centrally retriangulating a polytopal sphere with g₂≤ 1 along a certain subcomplex. This implies that all homology manifolds with g₂=2 are polytopal spheres.

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