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Projectivities in simplicial complexes and colorings of simple polytopes

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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.

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Received: 28 February 2001 / in final form: 18 May 2001/Published online: 28 February 2002

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Joswig, M. Projectivities in simplicial complexes and colorings of simple polytopes. Math Z 240, 243–259 (2002). https://doi.org/10.1007/s002090100381

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Keywords

  • Finite Group
  • Simplicial Complex
  • Coloring Problem
  • Toric Manifold
  • Simple Polytopes