Knot concordance and heegaard floer homology invariants in branched covers

DOI10.2140/gt.2008.12.2249zbMath1149.57007arXivmath/0701460OpenAlexW3099406694MaRDI QIDQ945637

Daniel Ruberman, Sašo Strle, J. Elisenda Grigsby

Publication date: 17 September 2008

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701460

zbMATH Keywords

branched coversbranched coverHeegaard Floer homologyknot concordance\(\tau \)-invariantsmooth knot concordance

Mathematics Subject Classification ID

Related Items (21)

Obstructions to Lagrangian cobordisms between Legendrians via generating families ⋮ Filtering smooth concordance classes of topologically slice knots ⋮ Equivariant Seiberg-Witten-Floer cohomology ⋮ Concordance to links with unknotted components ⋮ Polynomial splittings of correction terms and doubly slice knots ⋮ Concordance invariants from higher order covers ⋮ A note on applications of the d-invariant and Donaldson's theorem ⋮ Topologically slice knots with nontrivial Alexander polynomial ⋮ An Ozsváth-Szabó Floer homology invariant of knots in a contact manifold ⋮ Spherical 3-manifolds bounding rational homology balls ⋮ Computing knot Floer homology in cyclic branched covers ⋮ Sums of Lens spaces bounding rational balls ⋮ Satellites of infinite rank in the smooth concordance group ⋮ THE ALGEBRAIC CONCORDANCE ORDER OF A KNOT ⋮ The concordance genus of a knot. II. ⋮ INVARIANTS FOR LEGENDRIAN KNOTS IN LENS SPACES ⋮ ON KNOTS WITH INFINITE SMOOTH CONCORDANCE ORDER ⋮ Connected Floer homology of covering involutions ⋮ Heegaard Floer homology and genus one, one-boundary component open books ⋮ Distinguishing topologically and smoothly doubly slice knots ⋮ Knot Floer homology and relative adjunction inequalities

Uses Software

• PARI/GP
• KnotInfo

Cites Work

• Unnamed Item
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• Knot concordance and torsion
• Rational homology spheres and the four-ball genus of knots
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• Torsion invariants of Spin\(^c\)-structures on 3-manifolds
• Structure in the classical knot concordance group
• Knot concordance, Whitney towers and \(L^2\)-signatures
• Knot Floer homology and the four-ball genus
• Obstructing four-torsion in the classical knot concordance group
• Holomorphic disks and topological invariants for closed three-manifolds
• An application of gauge theory to four dimensional topology
• Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary
• Holomorphic disks and knot invariants
• A combinatorial description of knot Floer homology
• On combinatorial link Floer homology
• Order in the concordance group and Heegaard-Floer homology
• Sums of Lens spaces bounding rational balls
• Holomorphic triangles and invariants for smooth four-manifolds
• ON KNOTS WITH INFINITE SMOOTH CONCORDANCE ORDER
• A Simple Proof that the Concordance Group of Algebraically Slice Knots is Infinitely Generated
• A Concordance Invariant from the Floer Homology of Double Branched Covers

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