Seifert manifolds and (1,1)-knots

Luigi Grasselli; Michele Mulazzani

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arXiv · math/0510318

Seifert manifolds and (1,1)-knots

Luigi Grasselli·Michele Mulazzani

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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.

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BibTeX RIS

Luigi Grasselli, Michele Mulazzani. 2005-10-15. Seifert manifolds and (1,1)-knots. https://arxiv.org/abs/math/0510318

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