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Colorings of simplicial complexes

Special Events

Speaker: Michael Joswig, Universitat Magdeburg/ TU Berlin, Germany
Location: 693 Kerr
Start time: Wed, Dec 3 2003, 4:10PM

We introduce the group of projectivities of a d-dimensional simplicial complex. It is easy to show that for "reasonable" complexes the non-triviality of this group is the obstruction to d-colorability of the 1-skeleton (in the usual graph-theoretic sense). A first key result indicates how to compute this group at least in certain cases. Applications include the classical art gallery problem, a (known) reformulation of the 4-color theorem, and the construction of 3-manifolds via branched coverings.

This is a joint Colloquium/ Geometry-Topology seminar