Logistics

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.

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.

References:

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. https://web.ma.utexas.edu/users/dafr/bordism.pdf
Adams, The knot book.

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

Extra material

Quiz about first half of the class

 

Exercise class:   given by Eilind Karlsson