Dan Edidin : Inertial products, Chern classes and exotic operations in K-theory

Posted by Mihnea Popa , part of the Algebraic Geometry Seminar.

At

Nov. 7, 2012, 4 p.m.

In

SEO 427

Abstract

Given a group acting properly on a smooth variety $X$, we show how to define a family inertial products, Chern classes and operations (Adams, $\lambda$, $\psi$) on the rational $K$-theory of the associated inertia stack $I {\mathcal X}$. We give a conjectural relationship between certain of these inertial operations and operations on the classical $K$-theory of a resolution of singularities of moduli space of the cotangent bundle stack $T^*{\mathcal X}$. Finally we give some toric examples where the relationship holds. This is joint work with Tyler Jarvis and Takashi Kimura.