Axiomatic TQFT, Axiomatic DQFT, and Exotic 4-Manifolds
Published in Quantum Topology (submitted), 2011
We prove that any unitary, axiomatic topological quantum field theory in four dimensions cannot detect changes in the smooth structure of a simply connected, closed, oriented smooth manifold M. However, Donaldson–Witten theory (a TQFT but not axiomatic) can detect such changes. We resolve this by introducing a new set of axioms for a “differential quantum field theory” that slightly modify the naturality and functoriality axioms of TQFT so that a theory may detect changes in smooth structure.
Recommended citation: Kelly Davis. (2011). "Axiomatic TQFT, Axiomatic DQFT, and Exotic 4-Manifolds." Quantum Topology (submitted).
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