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Shellings of simplicial balls and P.L. manifolds with boundary

✍ Scribed by Udo Pachner

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
650 KB
Volume
81
Category
Article
ISSN
0012-365X

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✦ Synopsis

Shellability of simplicial complexes has been a powerful concept in polyhydral theory, in p.1. topology and recently in connection with Cohen-Macaulay rings. It is known that all 2-spheres and all boundary complexes of convex polytopes are shellable. The analogous theorem fails for general simplicial balls and spheres.

In this paper we study transformations of simplicial p.l. manifolds by elementary boundary operations (shellings and inverse shellings) and bistellar operations (the inner equivalent to shellings).

It is shown that a simplicial p.l. manifold A can be transformed in any other simplicial p.l. manifold A' homeomorphic to A using these elementary operations.

In the case of balls only elementary boundary operations are needed.

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