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A Burau–Alexander 2-functor on tangles

Volume 240 / 2018

David Cimasoni, Anthony Conway Fundamenta Mathematicae 240 (2018), 51-79 MSC: Primary 57M25; Secondary 18D05. DOI: 10.4064/fm274-11-2016 Published online: 4 May 2017

Abstract

We construct a weak $2$-functor from the bicategory of oriented tangles to a bicategory of Lagrangian cospans. This functor simultaneously extends the Burau representation of the braid groups, its generalization to tangles due to Turaev and the first-named author, and the Alexander module of $1$- and $2$-dimensional links.

Authors

  • David CimasoniSection de mathématiques
    Université de Genève
    2 rue du Lièvre
    1211 Genève, Switzerland
    e-mail
  • Anthony ConwaySection de mathématiques
    Université de Genève
    2 rue du Lièvre
    1211 Genève, Switzerland
    e-mail

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