The knot Floer complex and the smooth concordance group

Abstract

We define a new smooth concordance homomorphism based on the knot Floer complex and an associated concordance invariant, epsilon. As an application, we show that an infinite family of topologically slice knots are independent in the smooth concordance group.

25 pages, 5 figures

References in corpus (3)

• Floer homology and knot complements
• On knot Floer homology and cabling II
• Instantons, concordance, and Whitehead doubling

Cited by in corpus (33)

• Concordance homomorphisms from knot Floer homology
• Filtering smooth concordance classes of topologically slice knots
• Involutive Heegaard Floer homology
• The reduced knot Floer complex
• Four-ball genus bounds and a refinement of the Ozsvath-Szabo tau-invariant
• Casson towers and filtrations of the smooth knot concordance group
• Splicing knot complements and bordered Floer homology
• Connected sums and involutive knot Floer homology
• More concordance homomorphisms from knot Floer homology
• Satellite operators with distinct iterates in smooth concordance
• An infinite-rank summand of the homology cobordism group
• On rational sliceness of Miyazaki's fibered, $-$amphicheiral knots
• Linear independence of rationally slice knots
• The genus filtration in the smooth concordance group
• Branched covers bounding rational homology balls
• A restriction on the Alexander polynomials of $L$-space knots
• An adjunction inequality for the Bauer-Furuta type invariants, with applications to sliceness and 4-manifold topology
• Using secondary Upsilon invariants to rule out stable equivalence of knot complexes
• A connected sum formula for involutive Heegaard Floer homology
• Cable knots are not thin
• An infinite rank summand of topologically slice knots
• Rasmussen invariants of Whitehead doubles and other satellites
• Homology concordance and knot Floer homology
• Transverse and Legendrian invariants of cables in combinatorial link Floer homology
• Linear independence of cables in the knot concordance group
• Links with nontrivial Alexander polynomial which are topologically concordant to the Hopf link
• A note on the concordance invariants epsilon and upsilon
• Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex
• Twisted Mazur pattern satellite knots and bordered Floer theory
• Knot Floer Filtration Classes of Topologically Slice Knots
• A Combinatorial Description of the Knot Concordance Invariant Epsilon
• Framed instanton homology and concordance, II
• One-bipolar topologically slice knots and primary decomposition