Tsukuba Journal of Mathematics

On the structure of Takahashi manifolds

Beatrice Ruini and Fulvia Spaggiari

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We study the topological structure of the closed orientable 3-manifolds obtained by Dehn surgeries along certain links, first considered by Takahashi in [23]. The interest about such manifolds arises from the fact that they include well-known families of 3-manifolds, previously studied by several authors, as the Fibonacci manifolds [7], [10], [11], the Fractional Fibonacci manifolds [14], and the Sieradski manifolds [5], [6], respectively. Our main result states that the Takahashi manifolds are 2-fold coverings of the 3-sphere branched along the closures of specified 3-string braids. We also describe many of the above-mentioned manifolds as n-fold cyclic branched coverings of the 3-sphere.

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Tsukuba J. Math., Volume 22, Number 3 (1998), 723-739.

First available in Project Euclid: 30 May 2017

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Ruini, Beatrice; Spaggiari, Fulvia. On the structure of Takahashi manifolds. Tsukuba J. Math. 22 (1998), no. 3, 723--739. doi:10.21099/tkbjm/1496163675. https://projecteuclid.org/euclid.tkbjm/1496163675

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