Milnor Invariants and the HOMFLYPT Polynomial

Jean-Baptists Meilhan (Université Grenoble)

Monday 8th February, 2016 16:00-17:00 Maths 522


The purpose of this talk is to present a formula relating two link invariants of rather different nature: Milnor invariants (which is a 'classical' invariant, extracted from the lower central series of the fundamental group of the complement) and the HOMFLYPT polynomial (which is a 'quantum' invariant). After briefly reviewing the definitions, we will show how Milnor invariants of a link in the 3-sphere can be represented as a combination of HOMFLYPT polynomial of knots obtained from the link by various band sum operations. This is a joint work with Akira Yasuhara.

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