Slopes and signatures of links

Degtyarev, A., Florens, V. and Lecuona, A. G. (2022) Slopes and signatures of links. Fundamenta Mathematicae, 258(1), pp. 65-114. (doi: 10.4064/fm136-1-2022)

Abstract

We define the slope of a colored link in an integral homology sphere, associated to admissible characters on the link group. Away from a certain singular locus, the slope is a rational function which can be regarded as a multivariate generalization of the Kojima–Yamasaki η -function. It is the ratio of two Conway potentials, provided that the latter makes sense; otherwise, it is a new invariant. The slope is responsible for an extra correction term in the signature formula for the splice of two links, in the previously open exceptional case where both characters are admissible. Using a similar construction for a special class of tangles, we formulate generalized skein relations for the signature.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Garcia Lecuona, Professor Ana
• Authors: Degtyarev, A., Florens, V., and Lecuona, A. G.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Fundamenta Mathematicae
• Publisher: Instytut Matematyczny
• ISSN: 0016-2736
• ISSN (Online): 1730-6329
• Published Online: 14 March 2022
• Copyright Holders: Copyright © 2022 IMPAN
• First Published: First published in Fundamenta Mathematicae 258(1): 65-114
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

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