Combinatorial triangulations of homology spheres

Bagchi, Bhaskar ; Datta, Basudeb (2005) Combinatorial triangulations of homology spheres Discrete Mathematics, 305 (1-3). pp. 1-17. ISSN 0012-365X

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Let Mu be an n-vertex combinatorial triangulation of a Ζ2-homology d-sphere. In this paper we prove that if n ≤ d+8 then Mu must be a combinatorial sphere. Further, if n=d+9 and M is not a combinatorial sphere then Mu cannot admit any proper bistellar move. Existence of a 12-vertex triangulation of the lens space L(3,1) shows that the first result is sharp in dimension three. In the course of the proof we also show that anyΖ2-acyclic simplicial complex on ≤7 vertices is necessarily collapsible. This result is best possible since there exist 8-vertex triangulations of the Dunce Hat which are not collapsible.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Combinatorial Spheres; pl Manifolds; Collapsible Simplicial Complexes; Homology Spheres
ID Code:1006
Deposited On:25 Sep 2010 11:23
Last Modified:16 May 2016 12:11

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