## Osaka Journal of Mathematics

### On the generalized Dunwoody $3$-manifolds

#### Abstract

We introduce a family of orientable $3$-manifolds induced by certain cyclically presented groups and show that this family of $3$-manifolds contains all Dunwoody $3$-manifolds by using the planar graphs corresponding to the polyhedral description of the $3$-manifolds. As applications, we consider two families of cyclically presented groups, and show that these are isomorphic to the fundamental groups of the certain Dunwoody $3$-manifolds $D_{n}$ ($n \geq 2$) which are the $n$-fold cyclic coverings of the $3$-sphere branched over the certain two-bridge knots, and that $D_{n}$ is the $(\mathbb{Z}_{n}\oplus \mathbb{Z}_{2})$-fold covering of the $3$-sphere branched over two different $\Theta$-curves.

#### Article information

Source
Osaka J. Math., Volume 50, Number 2 (2013), 457-476.

Dates
First available in Project Euclid: 21 June 2013

https://projecteuclid.org/euclid.ojm/1371833495

Mathematical Reviews number (MathSciNet)
MR3080810

Zentralblatt MATH identifier
1270.57010

#### Citation

Kim, Soo Hwan; Kim, Yangkok. On the generalized Dunwoody $3$-manifolds. Osaka J. Math. 50 (2013), no. 2, 457--476. https://projecteuclid.org/euclid.ojm/1371833495

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