Knot homology groups from instantons

Abstract

For each partial flag manifold of SU(N), we define a Floer homology theory for knots in 3-manifolds, using instantons with codimension-2 singularities.

118 pages, 1 figure. v2: Further acknowledgements

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Cited by in corpus (74)

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• Knots, sutures and excision
• Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants
• Instantons and L-space surgeries
• The pillowcase and perturbations of traceless representations of knot groups
• Floer theory and flips
• Instanton Floer homology, sutures, and Heegaard diagrams
• Generic deformations of the colored sl(N)-homology for links
• A sheaf-theoretic model for SL(2,C) Floer homology
• Chern-Simons functional, singular instantons, and the four-dimensional clasp number
• Equivariant colored sl(N)-homology for links
• Chern-Simons Functional and the Homology Cobordism Group
• Representation spaces of pretzel knots
• A class of knots with simple $SU(2)$ representations
• SU(2)-cyclic surgeries and the pillowcase
• Traceless SU(2) representations of 2-stranded tangles
• A deformation of instanton homology for webs
• Floer field theory for tangles
• Immersed curves in Khovanov homology
• Tait colorings, and an instanton homology for webs and foams
• Khovanov homology is an unknot-detector
• Instanton L-spaces and splicing
• Instantons and some concordance invariants of knots
• Instanton Floer homology of almost-rational plumbings
• The Moduli Problem of Lobb and Zentner and the Coloured sl(N) Graph Invariant
• A sheaf-theoretic SL(2,C) Floer homology for knots
• The pillowcase and traceless representations of knot groups II: a Lagrangian-Floer theory in the pillowcase
• Holonomy perturbations in a cylinder, and regularity for traceless SU(2) character varieties of tangles
• A Generalization of the Tristram-Levine Knot Signatures as a Singular Furuta-Ohta Invariant for Tori
• Instanton Floer homology, sutures, and Euler characteristics
• Toroidal homology spheres and SU(2)-representations
• Equivariant aspects of singular instanton Floer homology
• Reconstructing GKZ via topological recursion
• Strong Khovanov-Floer Theories and Functoriality
• Link homology and equivariant gauge theory
• A hitchhiker's guide to Khovanov homology
• Khovanov homology of alternating links and SU(2) representations of the link group
• The quantum sl(n) graph invariant and a moduli space
• Non-orientable link cobordisms and torsion order in Floer homologies
• Sutured Manifolds and Polynomial Invariants from Higher Rank Bundles
• Tracefree $\mathrm{SL}(2,\mathbb{C})$-representations of Montesinos links
• Nilpotency in instanton homology, and the framed instanton homology of a surface times a circle
• Holonomy perturbations of the Chern-Simons functional for lens spaces
• Instantons, special cycles, and knot concordance
• Knot surgery formulae for instanton Floer homology II: applications
• The Fukaya category of the pillowcase, traceless character varieties, and Khovanov Cohomology
• The SU(N) Casson-Lin invariants for links
• Localization of a $K{O}^{\ast }(\text{pt})$-valued index and the orientability of the $Pi{n}^{-}(2)$ monopole moduli space
• Involutions, knots, and Floer K-theory
• The SU(2) Casson-Lin invariant of the Hopf link
• Equivariant Cerf theory and perturbative $SU(n)$ Casson invariants
• Instantons, Bar-Natan homology, and some concordance invariants of knots
• 3-manifolds without any embedding in symplectic 4-manifolds
• Instanton knot invariants with rational holonomy parameters and an application for torus knot groups
• Relations in singular instanton homology
• Knot Floer homology and the fundamental group of $(1,1)$ knots
• Instantons and Khovanov homology in ${\mathbb{RP}}^3$
• Torus knots, the A-polynomial, and SL(2,C)
• 2-torsion in instanton Floer homology
• A symplectic formula of generalized Casson invariants
• A Casson-Lin type invariant for links
• On the Classification of Topological Quandles
• Traceless Character Varieties, the Link Surgeries Spectral Sequence, and Khovanov Homology
• A Floer homology invariant for $3$-orbifolds via bordered Floer theory
• On the Kronheimer-Mrowka concordance invariant
• The SO(3) Vortex Equations over Orbifold Riemann Surfaces
• Tait coloring and a moduli space
• Framed instanton homology and concordance, II
• Knot surgery formulae for instanton Floer homology I: the main theorem