A Lagrangian representation of tangles

Cimasoni, David; Turaev, Vladimir

doi:10.1016/j.top.2005.01.001

Scientific article

English

A Lagrangian representation of tangles

ContributorsCimasoni, David

; Turaev, Vladimir

Published inTopology, vol. 44, no. 4, p. 747-767

Publication date2005

Abstract

We construct a functor from the category of oriented tangles in R^3 to the category of Hermitian modules and Lagrangian relations over Z[t,t^{-1}]. This functor extends the Burau representations of the braid groups and its generalization to string links due to Le Dimet.

Keywords

Braids
Tangles
String links
Burau representation
Lagrangian relations

Classification

arxiv : math.GT

Affiliation entities

Faculté des sciences / Section de mathématiques

Citation (ISO format)

CIMASONI, David, TURAEV, Vladimir. A Lagrangian representation of tangles. In: Topology, 2005, vol. 44, n° 4, p. 747–767. doi: 10.1016/j.top.2005.01.001

Article (Accepted version)

Identifiers

PID : unige:12206
DOI : 10.1016/j.top.2005.01.001
arXiv : math/0406269v1

Journal ISSN0040-9383

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A Lagrangian representation of tangles

We construct a functor from the category of oriented tangles in R^3 to the category of Hermitian modules and Lagrangian relations over Z[t,t^{-1}]. This functor extends the Burau representations of the braid groups and its generalization to string links due to Le Dimet.

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