K-classes of matroids and equivariant localization

Details K-classes of matroids and equivariant localization K-classes of matroids and equivariant localization

2010-04-14

arxiv.org/abs/1004.2403v2

Mathematics

Combinatorics

v2: added a starting point for combinatorialists in Section 2.4, + minor changes

Scientific paper

To every matroid, we associate a class in the K-theory of the Grassmannian. We study this class using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial. We also extend results of the second author concerning the behavior of such classes under direct sum, series and parallel connection and two-sum; these results were previously only established for realizable matroids, and their earlier proofs were more difficult.

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