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

Bagchi, Bhaskar ; Datta, Basudeb (2008) Uniqueness of Walkup's 9-vertex 3-dimensional Klein bottle Discrete Mathematics, 308 (22). pp. 5087-5095. ISSN 0012-365X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00123...

Related URL: http://dx.doi.org/10.1016/j.disc.2007.09.030


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 K39 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:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Combinatorial 3-Manifolds; pl Manifolds; Bistellar Moves
ID Code:989
Deposited On:25 Sep 2010 06:31
Last Modified:16 May 2016 12:10

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