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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A peculiar triangulation of the $ 3$-sphere

Author: A. Altshuler
Journal: Proc. Amer. Math. Soc. 54 (1976), 449-452
MathSciNet review: 0397744
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Abstract: A triangulation of the $ 3$-sphere with $ 10$ vertices is presented, which is not directly obtainable by a generalized stellar subdivision from any $ 3$-sphere with $ 9$ vertices. This answers in the affirmative a conjecture by B. Grünbaum. This example is shown to be the minimal possible.

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Keywords: (Abstract) simplicial $ n$-complex, combinatorial $ n$-sphere, directly obtainable, shellable sphere
Article copyright: © Copyright 1976 American Mathematical Society

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