Bordisms and Topological Field Theories SS 2021



Time and place:

Tue 10:15 -- 12:00
Wed 10:15 -- 12:00

Both lectures and exercises will be given in a live stream.

More information can be found on the course moodle.

No lecture on Tuesday, May 11

On June 1 kindly Eilind Karlsson will give one hour of lecture in the usual slot 10:15 - 11:00 and the exercise session fdirectly afterwards 11 - 11:45 instead of on Wednesday. On June 2 we will have two hours of lectures.

Due to the current situation with Covid-19, the lectures will be held via online stream. Read the following information HERE about online lectures before joining the class. Please register for the class on TUMonline. The link to the lectures is provided in moodle and will also be sent to registered participants via TUMonline. We will discuss the logistics on the class on Tuesday, April 13. If you cannot join then, or have trouble registering for the course, please contact me via email. 

Topic of course

Studying manifolds up to diffeomorphism is very difficult. However, if we instead study manifolds up to “cobordism” and consider the disjoint union we obtain very computable groups. In fact, product of manifolds gives a cobordism ring. In the 1980’s, Atiyah and Segal realized that the notion of cobordism naturally appears when decribing topological field theories mathematically. In the course we will encounter these notions.


Some references:
Michael Atiyah, Topological quantum field theories. IHES Publ. Math., (68):175–186 (1989), 1988.
Joachim Kock, Frobenius algebras and 2D topological quantum field theories
Christian Kassel, Marc Rosso, and Vladimir Turaev, Quantum groups and knot invariants
Daniel S. Freed, Bordism: Old and new.
Adams, The knot book.

References for manifolds:
Hirsch, Differential Topology
Kosinski, Differential Manifolds
(both available via TUM library)

Questions about classification of 2d oriented TFTs

Exercise classes

Exercise class:   given by Eilind Karlsson