Bagchi, Bhaskar and Datta, Basudeb and Spreer, Jonathan
(2016)
*Tight triangulations of closed 3-manifolds.*
In: EUROPEAN JOURNAL OF COMBINATORICS, 54
.
pp. 103-120.

PDF
Eur_Jou_Com_54_103_2016.pdf - Published Version Restricted to Registered users only Download (448kB) | Request a copy |

## Abstract

A triangulation of a closed 2-manifold is tight with respect to a field of characteristic two if and only if it is neighbourly; and it is tight with respect to a field of odd characteristic if and only if it is neighbourly and orientable. No such characterization of tightness was previously known for higher dimensional manifolds. In this paper, we prove that a triangulation of a closed 3-manifold is tight with respect to a field of odd characteristic if and only if it is neighbourly, orientable and stacked. In consequence, the Kuhnel-Lutz conjecture is valid in dimension three for fields of odd characteristic. Next let F be a field of characteristic two. It is known that, in this case, any neighbourly and stacked triangulation of a closed 3-manifold is F-tight. For closed, triangulated 3-manifolds with at most 71 vertices or with first Betti number at most 188, we show that the converse is true. But the possibility of the existence of an F-tight, non-stacked triangulation on a larger number of vertices remains open. We prove the following upper bound theorem on such triangulations. If an F-tight triangulation of a closed 3-manifold has n vertices and first Betti number beta(1), then (n - 4) (617n - 3861) <= 15444 beta(1). Equality holds here if and only if all the vertex links of the triangulation are connected sums of boundary complexes of icosahedra. (C) 2015 Elsevier Ltd. All rights reserved.

Item Type: | Journal Article |
---|---|

Additional Information: | Copy right for this article belongs to the ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 24-28 OVAL RD, LONDON NW1 7DX, ENGLAND |

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

Depositing User: | Id for Latest eprints |

Date Deposited: | 02 Apr 2016 07:03 |

Last Modified: | 02 Apr 2016 07:03 |

URI: | http://eprints.iisc.ac.in/id/eprint/53573 |

### Actions (login required)

View Item |