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