Floer field theory for tangles

Abstract

We use quilted Floer theory to construct functor-valued invariants of tangles arising from moduli spaces of flat bundles on punctured surfaces. As an application, we show the non-triviality of certain elements in the symplectic mapping class groups of moduli spaces of flat bundles on punctured spheres.

Added result about smooth isotopy of squares of Dehn twists

References in corpus (4)

• Orientations for pseudoholomorphic quilts
• Symplectic topology of SU(2)-representation varieties and link homology, I: Symplectic braid action and the first Chern class
• A-infinity functors for Lagrangian correspondences
• Recursive relations in the cohomology rings of moduli spaces of rank 2 parabolic bundles on the Riemann sphere

Cited by in corpus (3)

• A-infinity functors for Lagrangian correspondences
• Generating the Fukaya categories of Hamiltonian G-manifolds
• $SO(3)$-Floer homology of 3-manifolds with boundary 1