Doodles and commutator identities
Geometric Topology
2021-02-25 v2
Abstract
A doodle is a collection of immersed circles without triple intersections in the -sphere. It was shown by the second author and P.~Tayler that doodles induce commutator identities (identities amongst commutators) in a free group. In this paper we observe this idea more closely by concentrating on doodles with proper noose systems and elementary commutator identities. In particular we show that there is a bijection between cobordism classes of colored doodles and weak equivalence classes of elementary commutator identities.
Cite
@article{arxiv.2006.08871,
title = {Doodles and commutator identities},
author = {Andrew Bartholomew and Roger Fenn and Naoko Kamada and Seiichi Kamada},
journal= {arXiv preprint arXiv:2006.08871},
year = {2021}
}