Concordance homomorphisms from knot Floer homology

Abstract

We modify the construction of knot Floer homology to produce a one-parameter family of homologies for knots in the three-sphere. These invariants can be used to give homomorphisms from the smooth concordance group to the integers, giving bounds on the four-ball genus and the concordance genus of knots. We give some applications of these homomorphisms.

Minor revision, corrected typos and added explanation to Chapter 8

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Cited by in corpus (72)

• New Quantum Obstructions to Sliceness
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• Optimal Cobordisms between Torus Knots
• Knot cobordisms, bridge index, and torsion in Floer homology
• More concordance homomorphisms from knot Floer homology
• Satellites of Infinite Rank in the Smooth Concordance Group
• Cabling in terms of immersed curves
• Knot Floer homology and the unknotting number
• On the Upsilon invariant and satellite knots
• The non-orientable 4-genus for knots with 8 or 9 crossings
• Upsilon-like concordance invariants from sl(n) knot cohomology
• On a Nonorientable Analogue of the Milnor Conjecture
• Non-slice linear combinations of iterated torus knots
• Signature and concordance of virtual knots
• On rational sliceness of Miyazaki's fibered, $-$amphicheiral knots
• On the Upsilon invariant of cable knots
• A survey of the homology cobordism group
• Linear independence of rationally slice knots
• Surgery exact triangles in involutive Heegaard Floer homology
• Genus one cobordisms between torus knots
• The ${\nu }^{+}$-equivalence classes of genus one knots
• Relative genus bounds in indefinite four-manifolds
• Instantons and some concordance invariants of knots
• The genus filtration in the smooth concordance group
• Almost simple linear graphs, homology cobordism and connected Heegaard Floer homology
• A full-twist inequality for the ${\nu }^{+}$-invariant
• Branched covers bounding rational homology balls
• Braids with as many full twists as strands realize the braid index
• The upsilon invariant at 1 of 3-braid knots
• Alternating numbers of torus knots with small braid index
• On the First Singularity for the Upsilon Invariant of Algebraic Knots
• Using secondary Upsilon invariants to rule out stable equivalence of knot complexes
• L-space knots have no essential Conway spheres
• An involutive upsilon knot invariant
• Categorical lifting of the Jones polynomial: a survey
• On the fractional Dehn twist coefficients of branched coverings
• On sums of torus knots concordant to alternating knots
• An adjunction inequality for the Bauer-Furuta type invariants, with applications to sliceness and 4-manifold topology
• Concordance invariant ${\rm Y}$ for balanced spatial graphs using grid homology
• A note on the four-dimensional clasp number of knots
• A slicing obstruction from the 10/8 theorem
• Upsilon type concordance invariants
• New Heegaard Floer slice genus and clasp number bounds
• An infinite rank summand of topologically slice knots
• Non-orientable link cobordisms and torsion order in Floer homologies
• Locally equivalent Floer complexes and unoriented link cobordisms
• Rasmussen invariants of Whitehead doubles and other satellites
• Unoriented Cobordism Maps on Link Floer Homology
• Upsilon invariants from cyclic branched covers
• Signature invariants related to the unknotting number
• Homology concordance and knot Floer homology
• Annular link invariants from the Sarkar-Seed-Szabó spectral sequence
• On independence of iterated Whitehead doubles in the knot concordance group
• Linear independence of cables in the knot concordance group
• On the Upsilon invariant of fibered knots and right-veering open books
• Nonorientable surfaces bounded by knots: a geography problem
• Hyperbolic L-space knots not concordant to algebraic knots
• Deformations of lattice cohomology and the upsilon invariant
• Instantons, Bar-Natan homology, and some concordance invariants of knots
• A cabling formula for ${\nu }^{+}$ invariant
• On the secondary Upsilon invariant
• Truncated Heegaard Floer Homology and Knot Concordance Invariants
• Links with nontrivial Alexander polynomial which are topologically concordant to the Hopf link
• A Floer homology invariant for $3$-orbifolds via bordered Floer theory
• A Combinatorial Description of the Knot Concordance Invariant Epsilon
• Cobordism distance on the projective space of the knot concordance group
• New family of hyperbolic knots whose Upsilon invariants are convex
• Non-orientable 4-genus of torus knots
• A family of concordance homomorphisms from Khovanov homology
• One-bipolar topologically slice knots and primary decomposition
• A note on the concordance invariants epsilon and upsilon