Instanton Floer homology for sutured manifolds with tangles

Abstract

We prove an excision theorem for the singular instanton Floer homology that allows the excision surfaces to intersect the singular locus. This is an extension of the non-singular excision theorem by Kronheimer and Mrowka and the genus-zero singular excision theorem by Street. We use the singular excision theorem to define an instanton Floer homology theory for sutured manifolds with tangles. As applications, we prove that the annular Khovanov homology (1) detects the unlink, (2) detects the closure of the trivial braid, and (3) distinguishes braid closures from other links; we also prove that the annular instanton Floer homology detects the Thurston norm of meridional surfaces.

arXiv comment50 pages, 1 figure

References in corpus (8)

• Categorification of the Kauffman bracket skein module of I-bundles over surfaces
• Floer homology and surface decompositions
• A Link Splitting Spectral Sequence in Khovanov Homology
• Khovanov module and the detection of unlinks
• Gauge theory and Rasmussen's invariant
• Rationality of Moduli Spaces of Parabolic Bundles
• Recursive relations for the cohomology ring of moduli spaces of stable bundles
• Instantons and Annular Khovanov Homology

Cited by in corpus (7)

• Instanton Floer homology, sutures, and Heegaard diagrams
• An enhanced Euler characteristic of sutured instanton homology
• Khovanov homology and the cinquefoil
• Knot Floer homology, link Floer homology and link detection
• Rank Bounds in Link Floer Homology and Detection Results
• Khovanov homology and causality in spacetimes
• Annular Khovanov homology and augmented links