Colored tangles and signatures
Geometric Topology
2017-02-16 v3
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 colored 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.
Cite
@article{arxiv.1507.07818,
title = {Colored tangles and signatures},
author = {David Cimasoni and Anthony Conway},
journal= {arXiv preprint arXiv:1507.07818},
year = {2017}
}
Comments
38 pages, 7 figures; final version, to appear in Math. Proc. Cambridge Philos. Soc