Seifert manifolds and (1,1)-knots

Details Seifert manifolds and (1,1)-knots Seifert manifolds and (1,1)-knots

2005-10-15

arxiv.org/abs/math/0510318v1

Mathematics

Geometric Topology

20 pages, 17 figures

Scientific paper

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.

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