Time and place

Lectures: Mon 14:15-16:00, Wed 13:15-14:00
Exercises: Wed 12:15-13:00
Seminar Room 02.08.011

Topic

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. You can find a syllabus here.

Lecture notes

Handwritten lecture notes will be available at this link and will be regularly updated throughout the semester.

References

Main references

1. Michael Atiyah, Topological quantum field theories. IHES Publ. Math., (68):175–186 (1989), 1988.
2. Joachim Kock, Frobenius algebras and 2D topological quantum field theories
3. Christian Kassel, Marc Rosso, and Vladimir Turaev, Quantum groups and knot invariants
4. Daniel S. Freed, Bordism: Old and new
5. Adams, The knot book.
6. Carqueville, Runkel, Lecture notes on field theory
7. Schweigert, Lecture notes on Hopf algebras, quantum groups, and topological field theory

References for manifolds

8. Hirsch, Differential Topology
9. Kosinski, Differential Manifolds (both available via TUM library)

Exercise classes

All the exercise sheets will be available on this page.