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Dehn surgeries on some classical links. (English) Zbl 1223.57005

In the present paper, the authors study the closed orientable \(3\)-manifolds obtained by Dehn surgery on some classical links, as the Borromean rings and twisted Whitehead links. They obtain geometric presentations for the fundamental groups of the constructed manifolds. The manifolds are described as \(2\)-fold branched coverings of the \(3\)-sphere with specific branched sets. As an application, they refine and give some additional information of the main theorem in M. Brittenham and Y.-Q. Wu [Commun. Anal. Geom. 9, No. 1, 97–113 (2001; Zbl 0964.57013)] for exceptional Dehn surgeries on 2-bridge knots.

MSC:

57M12 Low-dimensional topology of special (e.g., branched) coverings
57R65 Surgery and handlebodies
20F05 Generators, relations, and presentations of groups

Citations:

Zbl 0964.57013

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References:

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