**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.