Solvability of concordance groups and Milnor invariants

Alessio Di Prisa (Scuola Normale Superiore, Pisa)

Monday 22nd January 16:00-17:00 Maths 311B

Abstract

In this talk I will introduce the notions of concordance for several knotted objects in the 3-space, namely strongly invertible knots, theta curves and string links, and I will explain how the respective concordance groups of these objects are related to one another.

Using Milnor invariants, I will prove that the concordance group of 2-string links is not solvable. Exploiting the close relation between the objects mentioned above, it follows that the equivariant concordance group of strongly invertible knots and the cobordism group of theta curves are also not solvable.

Finally, I will show how these results can be used to answer a conjecture due to Kuzbary regarding the solvability of the quotient of the concordance group of n-string links modulo pure braids.

This is a joint work with G. Framba (Università di Pisa).

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