research-article

P.L. Homeomorphic Manifolds are Equivalent by Elementary Shellings

Author:

Udo PachnerAuthors Info & Claims

European Journal of Combinatorics, Volume 12, Issue 2

Pages 129 - 145

https://doi.org/10.1016/S0195-6698(13)80080-7

Published: 01 February 1991 Publication History

Abstract

Shellability of simplicial complexes has been a powerful concept in polyhedral theory, in p.l. topology and recently in connection with Cohen-Macaulay rings and toric varieties. It is well known that all 2-spheres and all boundary complexes of convex polytopes are shellable, but 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). As the main result we shall show that a simplicial p.l. manifold M can be transformed to any other simplical p.l. manifold M homeomorphic to M using these elementary operations. The tools we need and related results are summarized. In the last part we study generalized sheltings of totally strongly connected simplicial complexes and the effects on the face numbers of the complex.

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Index Terms

P.L. Homeomorphic Manifolds are Equivalent by Elementary Shellings
1. Mathematics of computing
  1. Discrete mathematics

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cover image European Journal of Combinatorics

European Journal of Combinatorics Volume 12, Issue 2

March 1991

90 pages

ISSN:0195-6698

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Copyright © Academic Press Limited.

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Academic Press Ltd.

United Kingdom

Publication History

Published: 01 February 1991

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Dunfield NObeidin MRudd C(2024)Computing a Link Diagram From Its ExteriorDiscrete & Computational Geometry10.1007/s00454-023-00533-w71:1(121-159)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s00454-023-00533-w
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Campen MSilva CZorin D(2016)Bijective maps from simplicial foliationsACM Transactions on Graphics10.1145/2897824.292589035:4(1-15)Online publication date: 11-Jul-2016
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