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 |
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Publication: | Discrete Mathematics |

Publisher: | Elsevier Science BV |

Additional Information: | Copyright for this article belongs to Elsevier. |

Keywords: | Combinatorial spheres; pl manifolds; Collapsible simplicial complexes; Homology spheres |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 02 Feb 2006 |

Last Modified: | 19 Sep 2010 04:23 |

URI: | http://eprints.iisc.ac.in/id/eprint/5280 |

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