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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.
Mathematische Zeitschrift – Springer Journals
Published: Jun 1, 2002
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