Mathematische Zeitschrift

, Volume 240, Issue 2, pp 243–259 | Cite as

Projectivities in simplicial complexes and colorings of simple polytopes

  • Michael Joswig
Original article


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Michael Joswig
    • 1
  1. 1.Institut für Mathematik, MA 6-2, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany, (e-mail: DE

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