On concordances in 3-manifolds
We describe an action of the concordance group of knots in the three-sphere 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...
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| Format: | Journal article |
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Wiley
2018
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| Zusammenfassung: | We describe an action of the concordance group of knots in the three-sphere 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 Ozsvath-Szabo-Rasmussen's tau-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 tau-invariants. |
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