Seifert manifolds and (1,1)-knots
Geometric Topology
2007-05-23 v1
Abstract
The aim of this paper is to investigate the relations between Seifert manifolds and (1,1)-knots. In particular, we prove that every orientable Seifert manifold with invariants {Oo,0|-1;(p,q),...,(p,q),(l, l-1)} has a cyclically presented fundamental group and, moreover, it is the n-fold strongly-cyclic covering of the lens space L(|nlq-p|,q), branched over the (1,1)-knot K(q,q(nl-2),p-2q,p-q) if p>=2q, and over the (1,1)-knot K(p-q,2q-p,q(nl-2),p-q) if p<2q.
Cite
@article{arxiv.math/0510318,
title = {Seifert manifolds and (1,1)-knots},
author = {Luigi Grasselli and Michele Mulazzani},
journal= {arXiv preprint arXiv:math/0510318},
year = {2007}
}
Comments
20 pages, 17 figures