Projectivities in simplicial complexes and colorings of simple polytopes
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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.
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