Concordance of links with identical Alexander invariants

Choon, Jae; Friedl, Stefan; Powell, Mark

doi:10.1112/blms/bdu002

Cited by 6 publications

(1 citation statement)

References 31 publications

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“…In other words, the Alexander polynomials of knots and links determine their topological concordance type in these cases. Interestingly, Cha, Friedl and Powell [CFP14] proved that these two cases are exceptional. Namely, they showed that the link concordance class is not determined by the Alexander polynomial in any other cases.…”

Section: Introductionmentioning

confidence: 98%

Links with non-trivial Alexander polynomial which are topologically concordant to the Hopf link

Kim

Krcatovich

Park

2019

Trans. Amer. Math. Soc.

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Section: Introductionmentioning

confidence: 98%

Links with non-trivial Alexander polynomial which are topologically concordant to the Hopf link

Kim

Krcatovich

Park

2019

Trans. Amer. Math. Soc.

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A Topological Approach to Cheeger‐Gromov Universal Bounds for von Neumann ρ‐Invariants

Choon

2015

Comm Pure Appl Math

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Using deep analytic methods, Cheeger and Gromov showed that for any smooth .4k 1/-manifold there is a universal bound for the von Neumann L 2 -invariants associated to arbitrary regular covers. We present a proof of the existence of a universal bound for topological .4k 1/-manifolds, using L 2 -signatures of bounding 4k-manifolds. We give explicit linear universal bounds for 3-manifolds in terms of triangulations, Heegaard splittings, and surgery descriptions. We show that our explicit bounds are asymptotically optimal. As an application, we give new lower bounds of the complexity of 3-manifolds that can be arbitrarily larger than previously known lower bounds. As ingredients of the proofs that seem interesting on their own, we develop a geometric construction of efficient 4-dimensional bordisms of 3-manifolds over a group and develop an algebraic topological notion of uniformly controlled chain homotopies.

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Two-torsion in the grope and solvable filtrations of knots

Jang

2017

Int. J. Math.

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We study knots of order 2 in the grope filtration {G h } and the solvable filtration {F h } of the knot concordance group. We show that, for any integer n ≥ 4, there are knots generating a Z ∞ 2 subgroup of G n /G n.5 . Considering the solvable filtration, our knots generate a Z ∞ 2 subgroup of F n /F n.5 (n ≥ 2) distinct from the subgroup generated by the previously known 2-torsion knots of Cochran, Harvey, and Leidy. We also present a result on the 2-torsion part in the Cochran, Harvey, and Leidy's primary decomposition of the solvable filtration.

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Concordance of links with identical Alexander invariants

Cited by 6 publications

References 31 publications

Links with non-trivial Alexander polynomial which are topologically concordant to the Hopf link

Links with non-trivial Alexander polynomial which are topologically concordant to the Hopf link

A Topological Approach to Cheeger‐Gromov Universal Bounds for von Neumann ρ‐Invariants

Two-torsion in the grope and solvable filtrations of knots

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