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Slopes and concordance of links

Alex Degtyarev, Vincent Florens and Ana G Lecuona

Algebraic & Geometric Topology 24 (2024) 1101–1120

The slope is an isotopy invariant of colored links with a distinguished component, initially introduced by the authors to describe an extra correction term in the computation of the signature of the splice. It appeared to be closely related to several classical invariants, such as the Conway potential function or the Kojima η–function (defined for two-components links). We prove that the slope is invariant under colored concordance of links. Besides, we present a formula to compute the slope in terms of C–complexes and generalized Seifert forms.

concordance, links, $C$–complexes, slope
Mathematical Subject Classification
Primary: 57K10, 57K14, 57N70
Received: 20 February 2022
Revised: 18 September 2022
Accepted: 4 October 2022
Published: 12 April 2024
Alex Degtyarev
Department of Mathematics
Bilkent University
Vincent Florens
Labaratoire de Mathématiques et leurs Applications
Université de Pau et des Pays de l’Adour
Ana G Lecuona
Aix Marseille Université, CNRS, Centrale Marseille
Institut de Mathématiques de Marseille
School of Mathematics and Statistics
University of Glasgow
United Kingdom

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