## Tsukuba Journal of Mathematics

### On periodic Takahashi manifolds

Michele Mulazzani

#### Abstract

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 $\bm{S}^{3}$), 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 $\bm{S}^{3}$.

#### Article information

Source
Tsukuba J. Math., Volume 25, Number 2 (2001), 229-237.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496164284

Digital Object Identifier
doi:10.21099/tkbjm/1496164284

Mathematical Reviews number (MathSciNet)
MR1869599

Zentralblatt MATH identifier
1010.57001

#### Citation

Mulazzani, Michele. On periodic Takahashi manifolds. Tsukuba J. Math. 25 (2001), no. 2, 229--237. doi:10.21099/tkbjm/1496164284. https://projecteuclid.org/euclid.tkbjm/1496164284