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Sem. Topologia Alg.

 

Torres formula for multivariable link signature


Prelegent: Maciej Markiewicz

2020-12-08 16:15

Multivariable Levine-Tristram signature is an invariant of links introduced by D.Cimasoni and V.Florens in their 2005 paper. It is a function from the m-th power of the unit complex circle with 1 removed to integers. It has an interpretation in terms of 4-dimensional topology via a formula which allows to calculate certain Casson-Gordon invariants of a manifold M produced by surgery on a link L from the multivariable signature of this link. However, this does not allow to calculate all of the Casson-Gordon invariants of M. Our goal is to generalize this formula by considering not just the multivariable signature, but also its limits as some of the variables tend to 1. One might expect that these limits are related to signatures of suitable sublinks and indeed, we prove how to relate these functions to each other, obtaining a Torres-type formula for the multivariable signature.