Date & Time: Friday, March 04, 2016, 15:30-17:30
Venue: Room No. 216

Title: Introduction to topological K-theory

Speaker: Sudarshan Gurjar, IIT Bombay

Abstract: The next two talks in the Geometry-Topology seminar (on 04/03/16 and 11/03/16) will be on introduction to the basics of topological K-theory. Topological K-theory attaches to each topological space, a ring gotten using isomorphism classes of topological vector bundles. In the first lecture, I will prove some basic facts about complex vector bundles on compact, Hausdorff spaces and introduce the K-groups. The second lecture will be largely devoted to sketching a proof of Bott periodicity; a central theorem in this subject. Two classical (and related) applications of this theorem are in proving non-parallelizability of spheres other than those of dimension 1,3 and 7 and non-existence of finite-dimensional division algebras over R except in dimensions 1,2, 4 and 8.