# K-homology and quantization commutes with reduction problem

## GAP Seminar

## Meeting Details

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**Speaker:** Song Yanli, Penn State University

**Abstract:** K-homology is the homology theory dual to Atiyah-Hirzebruch K-theory. Following a suggestion of Atiyah, Kasparov gave an analytic definition of K-homology using Fredholm operators. On the other hand, Baum and Douglas gave a geometric definition using spin-c manifolds, bordisms, and so on. Roughly speaking, the isomorphism between the geometrically and analytically-defined K-homology groups can be viewed as a generalization of geometric quantization. In this framework, the quantization commutes with reduction problem can be considered as the construction of a commutative diagram in (equivariant) K-homology. In this talk, I shall carry out the construction in the simplest case, where the group is a circle. This is joint work with Nigel Higson.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 10/04/2011

**Time:** 2:30pm - 3:20pm