Knotoids
Geometric Topology
2011-04-14 v5
Abstract
We introduce and study knotoids. Knotoids are represented by diagrams in a surface which differ from the usual knot diagrams in that the underlying curve is a segment rather than a circle. Knotoid diagrams are considered up to Reidemeister moves applied away from the endpoints of the underlying segment. We show that knotoids in generalize knots in and study the semigroup of knotoids. We also discuss applications to knots and invariants of knotoids.
Keywords
Cite
@article{arxiv.1002.4133,
title = {Knotoids},
author = {Vladimir Turaev},
journal= {arXiv preprint arXiv:1002.4133},
year = {2011}
}
Comments
27 pages, 7 figures. References updated