## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** The equivariant complex cobordism ring of a finite abelian group

**Speaker:** Will Abram

**Speaker Info:** University of Michigan

**Brief Description:**

**Special Note**:

**Abstract:**

The calculation of the non-equivariant cobordism ring due to Milnor and Quillen was one of the great successes of algebraic topology.
Equivariantly, Kriz described tom Dieck's stable equivariant complex
cobordism ring MU_G_*, in the case G = Z/p, as the pullback of a diagram of rings arising from the Tate diagram for MU_(Z/p). We extend this work to the case of G a finite abelian group, where we describe MU_G_* as the inverse limit over certain G-spectra F(S) indexed over chains of subgroups of G. In the case G = Z/p^n, we get a simple description of MU_G_* as the n-fold pullback of a diagram of rings. In the general case, we are still able to compute the algebraic structure of F(S)_* explicitly. I will discuss this computation in some detail.

**Date:** Monday, October 08, 2012

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Prof. Paul Goerss

**Contact email:** pgoerss@math.northwestern.edu

**Contact Phone:** 847-491-8544

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