# Equivariant K-theory and orbifold power operations

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Mathieu Stiénon, Nigel Higson, Ping Xu.

**Speaker:** Takashi Kimura, Boston University

**Abstract:** Associated to a smooth projective variety X with a proper action of a complex algebraic group G, conditions that insure that the quotient [X/G] is a complex orbifold, is its orbifold K-theory ring, a K-theoretic version of Chen-Ruan orbifold cohomology. Orbifold K-theory contains, as a subring, the ordinary equivariant K-theory of X, and is additively equal to the equivariant K-theory of the inertia manifold of X. In recent work with Edidin and Jarvis,
we show that under certain conditions orbifold K-theory (and its cousins) admit power (or Adams) operations which yields an exotic positive structure (that is, elements which are analogs of classes of vector bundles) on orbifold K-theory.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 03/13/2012

**Time:** 2:30pm - 3:30pm