Mathematical Research Letters

Volume 21 (2014)

Number 3

The genus two Goeritz group of $\mathbb{S}^2 \times \mathbb{S}^1$

Pages: 449 – 460



Sangbum Cho (Department of Mathematics Education, Hanyang University, Seoul, Korea)

Yuya Koda (Mathematical Institute, Tohoku University, Sendai, Japan)


The genus-$g$ Goeritz group is the group of isotopy classes of orientation-preserving homeomorphisms of a closed orientable $3$-manifold that preserve a given genus-$g$ Heegaard splitting of the manifold. In this work, we show that the genus-$2$ Goeritz group of $\mathbb{S}^2 \times \mathbb{S}^1$ is finitely presented, and give its explicit presentation.

2010 Mathematics Subject Classification

57M60, 57N10

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