Projectivities in simplicial complexes and colorings of simple polytopes

By Michael Joswig. 2001

68 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c148d5771e75714500eee1c63689aa4a43c29b60

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. V. Buchstaber
2. T. Panov
3. M. Masuda

In Discrete Mathematics and Combinatorics

1. T. Panov
2. V. Buchstaber
3. M. Masuda
4. Nigel Ray
5. D. Suh
6. S. Gitler
7. Frédéric Bosio
8. L. Meersseman

In Geometry and Topology

1. T. Panov
2. V. Buchstaber
3. M. Masuda
4. Nigel Ray
5. D. Suh
6. Frédéric Bosio
7. L. Meersseman
8. S. Theriault

Citations in the corpus

• Torus Actions and their Applications in Topology and Combinatorics (2002, background): “This is a classical result for n = 3; the proof in the general case can be found in [81].”