Floer field theory for coprime rank and degree

TL;DR

This paper develops a (2+1)-dimensional partial field theory using Lagrangian Floer theory on moduli spaces of unitary connections with coprime rank and degree, linking surfaces to Fukaya categories and bordisms to functors.

Contribution

It introduces a novel construction of category-valued field theories based on Floer theory in moduli spaces with coprime rank and degree, combining Cerf theory and quilt invariants.

Findings

Constructs Fukaya categories for moduli spaces of connections.

Defines functors between Fukaya categories for bordisms.

Establishes a new link between Floer theory and topological field theories.

Abstract

We construct partial category-valued field theories in (2+1)-dimensions using Lagrangian Floer theory in moduli spaces of central-curvature unitary connections with fixed determinant of rank r and degree d where r,d are coprime positive integers. These theories associate to a closed, connected, oriented surface the Fukaya category of the moduli space, and to a connected bordism between two surfaces a functor between the Fukaya categories. We obtain the latter by combining Cerf theory with holomorphic quilt invariants.