K-classes for matroids and equivariant localization

Abstract

To every matroid, we associate a class in the $K$-theory of the Grassmannian. We study this class by using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial. We also extend the second author’s results 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.