Projectivities in Simplicial Complexes and Colorings of Simple Polytopes

Details Projectivities in Simplicial Complexes and Colorings of Simple Polytopes Projectivities in Simplicial Complexes and Colorings of Simple Polytopes

2001-02-23

arxiv.org/abs/math/0102186v3

Mathematics

Combinatorics

16 pages, Latex2e

Scientific paper

For each strongly connected finite-dimensional (pure) simplicial complex we construct a finite group, the group of projectivities of the complex, which is a combinatorial but not a topological invariant. 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 algebraic varieties.

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