Fédération de Recherche Mathématiques des Pays de Loire

FR CNRS 2962


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Daniel RUBERMAN de Brandeis University - USA, est un expert en topologie des variétés de dimension 3,4, théorie de jauge, et la théorie des nœuds. Il est invité par Andreï PAJITNOV au Laboratoire de Mathématiques Jean Leray, à Nantes du 8 au 11 mai 2011, dans le cadre du projet GeanPyl. Il fera un exposé le 9 mai 14.00 -- 15.00 - Bâtiment 10 de Mathématiques - salle Eole.

Title: Applications of Heegaard-Floer theory to knot and link concordance

Abstract: Knots in the 3-sphere are said to be concordant if they co-bound an annulus in S3 x I; there is a similar definition for links. A knot is said to be slice if it is concordant to the trivial knot. There are really two equivalence relations that one can consider, depending on whether this annulus is to be smoothly or merely topologically embedded. Freedman's theorem that knots with trivial Alexander polynomial are topologically slice, together with Donaldson's theorem from gauge theory, imply that there is a difference between the topological and smooth cases. I will explain joint work with M. Hedden and C. Livingston, showing that there are knots that are topologically slice, yet not smoothly concordant to a knot with trivial Alexander polynomial. Related ideas give rise to subtle differences between smooth and topological link concordance. The proofs use invariants from Heegaard-Floer theory.