- Home »
- Invertible topological ﬁeld theories are SKK manifold invariants

Playing this video requires the latest flash player from Adobe.

Download link (right click and 'save-as') for playing in VLC or other compatible player.

Speaker(s):

Scientific Areas:

Collection/Series:

PIRSA Number:

18080048

Topological ﬁeld theories in the sense of Atiyah–Segal are symmetric monoidal functors from a bordism category to the category of complex (super) vector spaces. A ﬁeld theory E of dimension d associates vector spaces to closed (d-1)-manifolds and linear maps to manifolds of dimension d. It turns out that if E is invertible, i.e., if the vector spaces associated to (d-1)-manifolds have dimension one, then the complex number E(M) that E associates to a closed d-manifold M, is an SKK manifold invariant. Here these letters stand for schneiden=cut, kleben=glue and kontrolliert=controlled, meaning that E(M) does not change when modifying the manifold by cutting and gluing along hypersurfaces in a controlled way. The main result of this joint work with Matthias Kreck and Peter Teichner is that the map described above gives a bijection between topological ﬁeld theories and SKK manifold invariants.

©2012 Perimeter Institute for Theoretical Physics