##### Department of Mathematics,

University of California San Diego

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### Math 292: Topology seminar

## Anna Marie Bohmann

#### Vanderbilt University

## Multiplicative uniqueness of rational equivariant K-theory

##### Abstract:

Topological K-theory is one of the classical motivating examples of a commutative ring spectrum, and it has a natural equivariant generalization. The equivariant structure here has the strongest possible type of compatibility with the multiplication, making K-theory an example of a ``genuine-commutative" ring spectrum. There's quite a lot of structure involved here, so in order to understand it, we employ a classic strategy and rationalize. After rationalizing, we can use algebraic models due to Barnes--Greenlees--Kedziorek and to Wimmer to show that all of the additional ``norm" structure is determined by the equivariant homotopy groups and the underlying multiplication. This is joint work with Christy Hazel, Jocelyne Ishak, Magdalena Kedziorek, and Clover May.

Host: Zhouli Xu

### November 8, 2022

### 4:30 PM

APM 7218

Research Areas

Geometry and Topology****************************