Speaker: Mr. Cédric Dion
Affiliation: Ph.D. student at Université Laval
Date: 11/05/2022
Title: Arithmetic statistics for 2-bridge links
Abstract: Let p be a fixed odd prime number. A famous theorem due to Iwasawa gives a formula for the rate of growth of the p-class group when the fields vary in a Z_p-extension of a number field. In this talk, based on joint work with Anwesh Ray, we study the topological analogue of Iwasawa theory for knots or, more generally, for links which are disjoint union of knots. In this setting, one can show that the lambda-invariant associated to a Z_p-cover of a link with at least 2 components is always greater than 0. We give explicit formulae to detect when the case mu=0 and lambda=1 do occur, at least in the case of 2 and 3-components links. We then study the proportion of 2-component links for which mu=0 and lambda=1 when the links are parametrized in Schubert normal form. Backed by numerical evidence, we conjecture that mu=0 for 100% of such links.