Topology Date:  Friday, October 05, 2012 Location:  3088 East Hall (4:00 PM to 5:00 PM) Title:  The equivariant complex cobordism ring of a finite abelian group 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 $G = \mathbb{Z}/p$, as the pullback of a diagram of rings arising from the Tate diagram for $MU_{\mathbb{Z}/p}$. 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 $G = \mathbb{Z}/p^n$, 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. Speaker:  William Abram Institution:  University of Michigan Event Organizer:   Kriz      Edit this event (login required). Add new event (login required). For access requests and instructions, contact math-webmaster@umich.edu Back to previous page Back to UM Math seminars/events page.