The Euler class and some obstruction theory

Wednesday, September 16, 2015 - 16:00 to 16:51
Thackeray 427

Abstract or Additional Information

The Euler class is a certain characteristic class that appears in many parts of mathematics.  It can be found in the Gauss-Bonnet theorem, and it can be used to measure the twistedness of a real vector bundle.  I will provide a very hands on way of constructing this class and show how we can relate the Euler class to a generalization of the “Hairy Ball” theorem.  Along the way I will introduce some ideas from homotopy theory and obstruction theory that will be useful in this construction.  The aim of the talk is to be introductory and will assume very little background.