Uniqueness of Walkup's 9-vertex 3-dimensional Klein bottle

Bagchi, Bhaskar and Datta, Basudeb (2008) Uniqueness of Walkup's 9-vertex 3-dimensional Klein bottle. In: Discrete Mathematics, 308 (22). pp. 5087-5095.

PDF 9.pdf - Published Version Restricted to Registered users only Download (424kB) | Request a copy

Abstract

Via a computer search, Altshuler and Steinberg found that there are 1296+1 combinatorial 3-manifolds on nine vertices, of which only one is non-sphere. This exceptional 3-manifold View the MathML source triangulates the twisted S2-bundle over S1. It was first constructed by Walkup. In this paper, we present a computer-free proof of the uniqueness of this non-sphere combinatorial 3-manifold. As opposed to the computer-generated proof, ours does not require wading through all the 9-vertex 3-spheres. As a preliminary result, we also show that any 9-vertex combinatorial 3-manifold is equivalent by proper bistellar moves to a 9-vertex neighbourly 3-manifold.

Item Type:	Journal Article
Publication:	Discrete Mathematics
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Combinatorial 3-manifolds;pl Manifolds;Bistellar moves.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	12 Apr 2010 08:44
Last Modified:	19 Sep 2010 05:59
URI:	http://eprints.iisc.ac.in/id/eprint/26871

Actions (login required)

View Item