An Alexander type invariant for doodles
Geometric Topology
2020-09-21 v2
Abstract
We construct an Alexander type invariant for oriented doodles from a deformation of the Tits representation of the twin group and from the Chebyshev polynomials of second kind. Similar to the Alexander polynomial, our invariant vanishes on unlinked doodles with more than one component. We also include values of our invariant on several doodles.
Cite
@article{arxiv.2005.06290,
title = {An Alexander type invariant for doodles},
author = {Bruno Cisneros and Marcelo Flores and Jesús Juyumaya and Christopher Roque-Márquez},
journal= {arXiv preprint arXiv:2005.06290},
year = {2020}
}
Comments
37 pages, many figures. v2: typos and table corrected, conjecture of v1 omitted