On the structure of Takahashi manifolds (Q1293155)

The authors study the topology of Takahashi manifolds. A Takahashi manifold is a closed connected orientable oriented 3-manifold obtained by Dehn surgeries along a link which is a chain of unknotted components, and each component is oriented and linked with exactly two adjacent components. Remark that Fibonacci manifolds, fractional Fibonacci manifolds and Sieradski manifolds are Takahashi manifolds. In 1989 Takahashi gave a finite presentation of the fundamental group of Takahashi manifolds. The main result of the paper is a generalization of a well-known result for Fibonacci manifolds and fractional Fibonacci manifolds, and states that the Takahashi manifolds are 2-fold covering of the 3-sphere branched along the closure of specified 3-string braids. They also describe many of these manifolds as \(n\)-fold cyclic branched coverings of the 3-sphere.