Representations of (1,1)-knots
Geometric Topology
2007-05-23 v2
Abstract
We present two different representations of (1,1)-knots and study some connections between them. The first representation is algebraic: every (1,1)-knot is represented by an element of the pure mapping class group of the twice punctured torus. The second representation is parametric: every (1,1)-knot can be represented by a 4-tuple of integer parameters. The strict connection of this representation with the class of Dunwoody manifolds is illustrated. The above representations are explicitly obtained in some interesting cases, including two-bridge knots and torus knots.
Keywords
Cite
@article{arxiv.math/0501234,
title = {Representations of (1,1)-knots},
author = {Alessia Cattabriga and Michele Mulazzani},
journal= {arXiv preprint arXiv:math/0501234},
year = {2007}
}
Comments
16 pages, 7 figures. To appear in Fundamenta Mathematicae, special volume Proceedings of Knots in Poland, vol. II