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Coloured tangles and signatures

Published online by Cambridge University Press:  27 March 2017

DAVID CIMASONI  and
ANTHONY CONWAY
DAVID CIMASONI
Affiliation:
Section de Mathématiques, Université de Genève, 2-4, rue du Lièvre, CP 240, CH-1211 Genève 24, Suisse. e-mails: David.Cimasoni@unige.ch, Anthony.Conway@unige.ch
ANTHONY CONWAY
Affiliation:
Section de Mathématiques, Université de Genève, 2-4, rue du Lièvre, CP 240, CH-1211 Genève 24, Suisse. e-mails: David.Cimasoni@unige.ch, Anthony.Conway@unige.ch
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Abstract

Taking the signature of the closure of a braid defines a map from the braid group to the integers. In 2005, Gambaudo and Ghys expressed the homomorphism defect of this map in terms of the Meyer cocycle and the Burau representation. In the present paper, we simultaneously extend this result in two directions, considering the multivariable signature of the closure of a coloured tangle. The corresponding defect is expressed in terms of the Maslov index and of the Lagrangian functor defined by Turaev and the first-named author.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 164 , Issue 3 , May 2018 , pp. 493 - 530
Copyright
Copyright © Cambridge Philosophical Society 2017 

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