# Combinatorial triangulations of homology spheres

Bagchi, Bhaskar and Datta, Basudeb (2005) Combinatorial triangulations of homology spheres. In: Discrete Mathematics, 305 (1&3). pp. 1-17.

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## Abstract

Let M be an n-vertex combinatorial triangulation of a $Z_{2}$-homology d-sphere. In this paper we prove that if n \leq d + 8 then M must be a combinatorial sphere. Further, if n = d + 9 and M is not a combinatorial sphere then M 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 any $Z_{2}$-acyclic sitnplicial complex on \leq 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: Journal Article http://dx.doi.org/10.1016/j.disc.2005.06... Copyright for this article belongs to Elsevier. Combinatorial spheres; pl manifolds; Collapsible simplicial complexes; Homology spheres Division of Physical & Mathematical Sciences > Mathematics 02 Feb 2006 19 Sep 2010 04:23 http://eprints.iisc.ernet.in/id/eprint/5280