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Projectivities in simplicial complexes and colorings of simple polytopes

Projectivities in simplicial complexes and colorings of simple polytopes For each strongly connected finite-dimensional (pure) simplicial complex $\Delta$ we construct a finite group $\Pi(\Delta)$ , the group of projectivities of $\Delta$ , which is a combinatorial but not a topological invariant of $\Delta$ . This group is studied for combinatorial manifolds and, in particular, for polytopal simplicial spheres. The results are applied to a coloring problem for simplicial (or, dually, simple) polytopes which arises in the area of toric manifolds. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Projectivities in simplicial complexes and colorings of simple polytopes

Mathematische Zeitschrift , Volume 240 (2) – Jun 1, 2002

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References (23)

Publisher
Springer Journals
Copyright
Copyright © 2002 by Springer-Verlag Berlin Heidelberg
Subject
Legacy
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s002090100381
Publisher site
See Article on Publisher Site

Abstract

For each strongly connected finite-dimensional (pure) simplicial complex $\Delta$ we construct a finite group $\Pi(\Delta)$ , the group of projectivities of $\Delta$ , which is a combinatorial but not a topological invariant of $\Delta$ . This group is studied for combinatorial manifolds and, in particular, for polytopal simplicial spheres. The results are applied to a coloring problem for simplicial (or, dually, simple) polytopes which arises in the area of toric manifolds.

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jun 1, 2002

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