Monopoles and Landau-Ginzburg Models II: Floer Homology

Abstract

This is the second paper in this series. Following the setup of Meng-Taubes, we define the monopole Floer homology for any pair $(Y,\omega )$, where $Y$ is a compact oriented 3-manifold with toroidal boundary and $\omega$ is a suitable closed 2-form viewed as a decoration. This construction fits into a (3+1)-topological quantum field theory and generalizes the work of Kronheimer-Mrowka for closed oriented 3-manifolds. By a theorem of Meng-Taubes and Turaev, the Euler characteristic of this Floer homology recovers the Milnor-Turaev torsion invariant of the 3-manifold.

150 pages, 3 figures. v2 We add a finiteness result. v3 introduction revised

References in corpus (3)

• Floer homology and knot complements
• Algebra of the Infrared: String Field Theoretic Structures in Massive $\mathcal{N}=(2,2)$ Field Theory In Two Dimensions
• Monopoles and Landau-Ginzburg Models I

Cited by in corpus (2)

• Monopoles and Landau-Ginzburg Models I
• Monopoles and Landau-Ginzburg Models III: A Gluing Theorem