# CYCLES, COCYCLES, AND BICYCLES I

## GAP Seminar

## Meeting Details

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

**Speaker:** Paul Baum, Penn State University

**Abstract:** K-homology is the dual theory to K-theory. In algebraic geometry, the K-homology of an algebraic
variety X is the Grothendieck group of coherent algebraic sheaves on X. In topology, K-homology
is the homology theory determined by the Bott spectrum. These talks will develop a definition of
K-homology based K-cycles. The point will be made that all features of K-homology are then clearly
evident. In particular, a slight modification of the basic definition yields bicycles (i.e. bivariant cycles)
and thus produces bivariant K-theory.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 09/21/2010

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