EVENT DETAILS AND ABSTRACT

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.