In this paper we show that all 3-manifolds of a family introduced by M. J. Dunwoody are cyclic coverings of lens spaces (possibly S3), branched over genus one 1-bridge knots. As a consequence, we give a positive answer to the Dunwoody conjecture that all the elements of a wide subclass are cyclic coverings of S3 branched over a knot. Moreover, we show that all branched cyclic coverings of a 2-bridge knot belong to this subclass; this implies that the fundamental group of each branched cyclic covering of a 2-bridge knot admits a geometric cyclic presentation.

Genus one 1-bridge knots and Dunwoody manifolds / Grasselli, Luigi; M., Mulazzani. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - STAMPA. - 13:(2001), pp. 379-397.

Genus one 1-bridge knots and Dunwoody manifolds

GRASSELLI, Luigi;
2001-01-01

Abstract

In this paper we show that all 3-manifolds of a family introduced by M. J. Dunwoody are cyclic coverings of lens spaces (possibly S3), branched over genus one 1-bridge knots. As a consequence, we give a positive answer to the Dunwoody conjecture that all the elements of a wide subclass are cyclic coverings of S3 branched over a knot. Moreover, we show that all branched cyclic coverings of a 2-bridge knot belong to this subclass; this implies that the fundamental group of each branched cyclic covering of a 2-bridge knot admits a geometric cyclic presentation.
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379
397
Genus one 1-bridge knots and Dunwoody manifolds / Grasselli, Luigi; M., Mulazzani. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - STAMPA. - 13:(2001), pp. 379-397.
Grasselli, Luigi; M., Mulazzani
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/305296
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