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Topological quantum field theory.
18
votes
Accepted
Seiberg-Witten theory on 4-manifolds with boundary
Hi Fabian! Kronheimer and Mrowka's book Monopoles and three-manifolds lays out comprehensively the construction of a Seiberg-Witten TQFT, called monopole Floer homology.
It is conjectured to be isom …
17
votes
Cohomology rings and 2D TQFTs
There is indeed a Morse homology explanation; and, in the symplectic case, it's a degeneration of the Hamiltonian Floer cohomology picture. In a nutshell, you degenerate the surfaces to graphs, and th …