Orateur: Daniele Celoria (University of Oxford)
Titre: Almost-concordances in 3-manifolds
Résumé: We describe an action of the concordance group of knots in S^3 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 tau-invariant to obstruct
almost-concordances and prove that each L(p,1) admits infinitely many nullhomologous non almost-concordant knots.
We will then discuss some new developements due to Friedl-Nagel-Orson-Powell, and some genus bounds.

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