Short Ropes and Long Knots
Geometric Topology
2016-09-07 v2 Algebraic Topology
Abstract
A rope is a non-singular embedding of a closed interval into R^3, which sends the ends of the interval to some fixed points A and B such that |AB|=1. A rope is short if its length is less than 3. The main result of the paper is that the fundamental group of the space of short ropes is naturally isomorphic to the group completion of the semigroup of knots.
Keywords
Cite
@article{arxiv.math/9810040,
title = {Short Ropes and Long Knots},
author = {Jacob Mostovoy},
journal= {arXiv preprint arXiv:math/9810040},
year = {2016}
}
Comments
AMS-LaTeX, 15 pages, 9 figures. Version 2: some minor errors corrected