Algebraic Invariants of Links

Hillman, Jonathan A.

doi:10.1142/9789812776648

Cited by 85 publications

(103 citation statements)

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“…I thank T. Kohno for asking about the interpretation of my Milnor invariants in terms of Massey products. Finally, I am very grateful to J. Hillman for sending me his manuscript on algebraic invariants of links [Hil02] and for helpful communications.…”

Section: Acknowledgementsmentioning

confidence: 99%

Milnor invariants and Massey products for prime numbers

Morishita

2004

Compositio Math.

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Section: Acknowledgementsmentioning

confidence: 99%

Milnor invariants and Massey products for prime numbers

Morishita

2004

Compositio Math.

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“…Similar constructions and definitions have been previously considered by Rolfsen in (see also Hillman's book [, Section 1.5]).…”

Section: Introductionmentioning

confidence: 75%

On concordances in 3-manifolds

Celoria

2018

Journal of Topology

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We describe an action of the concordance group of knots in S3 on concordances of knots in arbitrary 3‐manifolds. As an application we define the notion of almost‐concordance between knots. After some basic results, we prove the existence of non‐trivial almost‐concordance classes in all non‐abelian 3‐manifolds. Afterwards, we focus the attention on the case of lens spaces, and use a modified version of the Ozsváth–Szabó–Rasmussen's τ‐invariant to obstruct almost‐concordances and prove that each L(p,1) admits infinitely many nullhomologous non almost‐concordant knots. Finally we prove an inequality involving the cobordism PL‐genus of a knot and its τ‐invariants, in the spirit of [Sarkar, Math. Res. Lett. 18 (2011) 1239–1257].

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“…To prove this assertion, we will use (a particular case of) the universal coefficient spectral sequence (UCSS) whose second page is given by E 2 p,q = Tor Λµ p (H q (M L ; Λ µ ), C λ ) and which converges to H * (M L ; C λ ), see [30,Chapter 2]. We start with the following claim.…”

Section: Proof Of Theorem 24mentioning

confidence: 99%