A two-category of Hamiltonian manifolds, and a (1+1+1) field theory

2019/03/26 by Cazassus, Guillem · 2 citations
#Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1903.10686

Abstract

We define an extended field theory in dimensions 1+1+1, that takes the form of a `quasi 2-functor' with values in a strict 2-category \widehatHam, defined as the `completion of a partial 2-category' Ham, notions which we define. Our construction extends Wehrheim and Woodward's Floer Field theory, and is inspired by Manolescu and Woodward's construction of symplectic instanton homology. It can be seen, in dimensions 1+1, as a real analog of a construction by Moore and Tachikawa. Our construction is motivated by instanton gauge theory in dimensions 3 and 4: we expect to promote \widehatHam to a (sort of) 3-category via equivariant Lagrangian Floer homology, and extend our quasi 2-functor to dimension 4, via equivariant analogues of Donaldson polynomials.

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• From multiplicative to additive geometry: deformation theory and 2D TQFT
• Lax-Kirchhoff moduli spaces and Hamiltonian 2D TQFT

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