On the structure of Takahashi manifolds

Abstract

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.