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Edward Swartz

Matroids and Quotients of Spheres

Abstract for the Combinatorics and Geometry/Topology Seminars 2000 February 3

The main theme is a connection between quotients of spheres by elementary abelian p-groups, and matroids representable over Zp . We will start with problems from Riemannian geometry in which quotient spaces of the form X=Sn/G, where G is an elementary abelian p-group, play an important role. Then we will show how to associate a matroid MX to X. Next we will see how MX gives a tremendous amount of information about the geometry and topology of X. Finally, the topology of X points us toward new results in matroid theory. These include new inequalities for the Tutte polynomial of a representable matroid, and a surprisingly simple relationship between the Mobius function of a matroid and whether or not it is affine.

seminars/comb/abstract.20000203.txt · Last modified: 2020/01/29 14:03 (external edit)