Seminar on Characteristic Classes

Sommersemester 2013

Prof. Dr. Anna Wienhard, Dr. Laura Schaposnik and Dr. Gye-Seon Lee

Time and Location
Thursdays 2 - 4 p.m. and INF 288, HS 1

Topic
Characteristic classes are invariants of fibre bundles or principal bundles on manifolds. They are important for the classification of manifolds. They also play an important role in differential geometry, gauge theory and related topics in physics. In this seminar we will introduce Stiefel-Whitney classes, the Euler class, Chern classes and Pontrjagin classes and study some of their properties. We will then discuss Chern-Weil theory, which describes how characteristic classes can be calculated using the curvature of the principal bundle. In the end we discuss an example of characteristic classes of flat bundles, due to Milnor, which shows us the limitations of Chern-Weil theory.

Prerequisites
Students should ideally have some background in algebraic topology and differential geometry. Interested students from physics are also welcome to attend. The seminar will be taught in english.

Organization
Students who would like to sign up for the seminar should send an email to Laura Schaposnik (schaposnik@mathi.uni-heidelberg.de) and let her know what talk they would like to give. If you are interested in one of the first talks, please be sure to contact her before the start of the semester. Once you have agreed on the date of your talk with Laura, you should contact the person who appears as advisor for your talk, Laura or Gye-Seon (lee@mathi.uni-heidelberg.de), to discuss the content of your talk in more detail. You should start preparing for your talk several weeks before you are scheduled to give speak. Please let Laura and Gye-Seon help you during the preparation.

Schedule

Date	Speaker	Title	Advisor
May 2	Sven	Vector bundles	Laura
May 9	Chr. Himmelf.
May 22	Laura	Homology and Cohomology	-
May 29	Axel	Axioms of Stiefel-Whitney and Chern classes	Laura
May 30	Fronleichnam
June 6	Gye-Seon	Constructions of Stiefel-Whitney and Chern classes	-
June 13	Tim	Pontrajagin classes and Pontrjagin numbers	Gye-Seon
June 20	Stephan	Chern-Weil theory I	Gye-Seon
July 11	Felipe	Chern-Weil theory II	Gye-Seon
July 18	Malte	Characteristic classes of flat bundles	Laura