Generalized Takahashi manifolds

Abstract

We introduce a family of closed 3-dimensional manifolds, which are a generalization of certain manifolds studied by M. Takahashi. The manifolds are represented by Dehn surgery with rational coefficients on the 3-sphere, along an n-periodic 2n-component link. A presentation of their fundamental group is obtained, and covering properties of these manifolds are studied. In particular, this family of manifolds includes the whole class of cyclic branched coverings of two-bridge knots. As a consequence we obtain a simple explicit surgery presentation for this important class of manifolds.