MERCOLEDI' 16 MAGGIO 2012
14:30-15:30, Sala Seminari (Dip. Matematica)
SEMINARI DI GEOMETRIAHigher dimensional Tutte polynomial
Sergei Chmutov (Ohio State University)
The Tutte polynomial for graphs can be generalized to the higher dimensional cell complexes. This was done recently by V.Krushkal and D.Renardy. It turns out that their polynomial is a particular case of the Tutte polynomial of some representable matroids. Thus it gives a topological interpretation for the combinatorial matroidal notions. I explain the relationship of the Tutte-Krushkal-Renardy polynomial with the other known results. In particular, I will show that evaluation of this polynomial at the origin gives the number of cellular spanning trees in a sense of A.Duval, C.Klivans and J.Martin. Moreover, a slight modification of the Krushkal-Renardy polynomial lead to the weighted cellular spanning trees and therefore can be calculated by the cellular matrix-tree theorem. In the case of cell decomposition of a sphere this modified polynomial also satisfies the duality relation of Krushkal-Renardy. Another specialization of the Tutte-Krushkal-Renardy polynomial is the Bott polynomials introduced by Raoul Bott in 1952. This is a joint work with C.Bajo and B.Burdick.