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2020•Annales de l’institut FourierOpen access

A multivariable Casson–Lin type invariant

Léo Bénard, Anthony Conway

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Abstract

We introduce a multivariable Casson–Lin type invariant for links in S 3 . This invariant is defined as a signed count of irreducible SU ( 2 ) representations of the link group with fixed meridional traces. For 2-component links with linking number one, the invariant is shown to be a sum of multivariable signatures. We also obtain some results concerning deformations of SU ( 2 ) representations of link groups.

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We introduce a multivariable Casson–Lin type invariant for links in S 3 . This invariant is defined as a signed count of irreducible SU ( 2 ) representations of the link group with fixed meridional traces. For 2-component links with linking number one, the invariant is shown to be a sum of multivariable signatures. We also obtain some results concerning deformations of SU ( 2 ) representations of link groups.

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Available abstract

We introduce a multivariable Casson–Lin type invariant for links in S 3 . This invariant is defined as a signed count of irreducible SU ( 2 ) representations of the link group with fixed meridional traces. For 2-component links with linking number one, the invariant is shown to be a sum of multivariable signatures. We also obtain some results concerning deformations of SU ( 2 ) representations of link groups.

Key concepts: Multivariable calculus, Invariant (physics), Mathematics, Pure mathematics, Zonal and meridional, Combinatorics, Physics, Mathematical physics

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