Rigidity and the Lower Bound Theorem for Doubly Cohen-Macaulay Complexes

We prove that for d 3, the 1-skeleton of any (d - 1)-dimensional doubly Cohen-Macaulay (abbreviated 2-CM) complex is generically drigid. This implies that Barnette's lower bound inequalities for boundary complexes of simplicial polytopes ([4],[3]) hold for every 2-CM complex of dimension 2 (see Kalai [8]). Moreover, the initial part (g0, g1, g2) of the g-vector of a 2-CM complex (of dimension 3) is an M-sequence. It was conjectured by Bj

• Type: Journal
• Year: 2008
• Where: DCG
• Authors: Eran Nevo
• Keywords: 2-CM Complex, Boundary Complexes, DCG 2008, Lower Bound