Marisa Hughes

Ph.D. (2013) Cornell University

First Position

Visiting Professor, Hamilton College

Dissertation

Quotients of Spheres by Linear Actions of Abelian Groups

Advisor

Edward Swartz

Research Area

matroids and topology

Abstract

We consider quotients of spheres by linear actions of real tori and finite abelian groups. To each quotient we associate a matroid or sequence of matroids. In the case of real tori, we find the integral homology groups of the resulting quotient spaces and singular sets in terms of the Tutte polynomial of the matroid(s). For finite groups, an algorithm for computing the Zp -homology of the quotient space is given.