We give a presentation of the n-dimensional oriented cobordism category Cob_n with generators corresponding to diffeomorphisms and surgeries along framed spheres, and a complete set of relations. Hence, given a functor F from the category of smooth oriented manifolds and diffeomorphisms to an arbitrary category C, and morphisms induced by surgeries along framed spheres, we obtain a necessary and sufficient set of relations these have to satisfy to extend to a functor from Cob_n to C. If C is symmetric and monoidal, then we also characterize when the extension is a TQFT.
Defining and classifying TQFTs via surgery
06.06.2018 14:15 - 16:00
Organiser:
N. Carqueville
Location: