Short Ropes and Long Knots

Details Short Ropes and Long Knots Short Ropes and Long Knots

1998-10-06

arxiv.org/abs/math/9810040v2

Mathematics

Geometric Topology

AMS-LaTeX, 15 pages, 9 figures. Version 2: some minor errors corrected

Scientific paper

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.

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