Seifert forms and concordance

Abstract

If a knot K has Seifert matrix V_K and has a prime power cyclic branched cover that is not a homology sphere, then there is an infinite family of non-concordant knots having Seifert matrix V_K.

Shortened version containing the main examples, published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper14.abs.html

Cited by in corpus (22)

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• Branched covers bounding rational homology balls
• Topological minimal genus and $L^2$-signatures
• Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials
• Embedding spheres in knot traces
• Knot concordance invariants from Seiberg-Witten theory and slice genus bounds in 4-manifolds
• Brieskorn spheres, cyclic group actions and the Milnor conjecture
• Upsilon invariants from cyclic branched covers
• Instantons, special cycles, and knot concordance
• Concordance invariants from higher order covers
• The $p$-adic limits of class numbers in ${\mathbb{Z}}_p$-towers
• Knots having the same Seifert form and primary decomposition of knot concordance
• Linear Independence of Knots Arising from Iterated Infection Without the Use of Tristram Levine Signatures
• Amenable signatures, algebraic solutions, and filtrations of the knot concordance group
• Polynomial splittings of metabelian von Neumann rho-invariants
• Higher-order Alexander invariants and filtrations of the knot concordance group
• Infinite family of non-concordant knots having the same Seifert form