Homotopy invariants of Gauss words
Geometric Topology
2009-05-11 v2
Abstract
By defining combinatorial moves, we can define an equivalence relation on Gauss words called homotopy. In this paper we define a homotopy invariant of Gauss words. We use this to show that there exist Gauss words that are not homotopically equivalent to the empty Gauss word, disproving a conjecture by Turaev. In fact, we show that there are an infinite number of equivalence classes of Gauss words under homotopy.
Cite
@article{arxiv.0902.0062,
title = {Homotopy invariants of Gauss words},
author = {Andrew Gibson},
journal= {arXiv preprint arXiv:0902.0062},
year = {2009}
}
Comments
15 pages, 4 figures. Second version: added reference, corrected some comments