On periodic Takahashi manifolds

Details On periodic Takahashi manifolds On periodic Takahashi manifolds

2001-04-24

arxiv.org/abs/math/0104224v1

Mathematics

Geometric Topology

12 pages, 5 figures. To appear in Tsukuba Journal of Mathematics

Scientific paper

In this paper we show that periodic Takahashi 3-manifolds are cyclic coverings of the connected sum of two lens spaces (possibly cyclic coverings of the 3-sphere), branched over knots. When the base space is a 3-sphere, we prove that the associated branching set is a two-bridge knot of genus one, and we determine its type. Moreover, a geometric cyclic presentation for the fundamental groups of these manifolds is obtained in several interesting cases, including the ones corresponding to the branched cyclic coverings of the 3-sphere.

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