Colloquium

Braids, mapping class groups, and homotopy groups

by Frederick Cohen, Professor of Mathematics,University of Rochester, New York

Abstract

This talk explores the connections between braidgroups, mapping class groups, and how these groupsencode maps between spheres. For example, elementary"cabling of braids" encodes information about mapsfrom large dimensional spheres to the 2-sphere. Themathematics is at the interface of low dimensionaltopology, homotopy theory, and Lie algebras. An overviewof how these different structures fit will be given. Thistalk is based on joint work with J. Berrick, Y.L. Wang,and J. Wu.