The aim of this paper is to investigate the relations between Seifert manifolds and (1,1)-knots. In particular, we prove that each orientable Seifert manifold with invariants{Oo,0| -1; (p,q),..., (p,q),(l, l-1)}, where (p,q) are taken n times, 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 a suitable (1,1)-knot.
Seifert manifolds and (1,1)-knots / Grasselli, Luigi; M., Mulazzani. - In: SIBERIAN MATHEMATICAL JOURNAL. - ISSN 0037-4466. - STAMPA. - 50:(2009), pp. 22-31. [10.1007/s11202-009-0003-x]
Seifert manifolds and (1,1)-knots
GRASSELLI, Luigi;
2009
Abstract
The aim of this paper is to investigate the relations between Seifert manifolds and (1,1)-knots. In particular, we prove that each orientable Seifert manifold with invariants{Oo,0| -1; (p,q),..., (p,q),(l, l-1)}, where (p,q) are taken n times, 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 a suitable (1,1)-knot.
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