Handlebody-preserving finite group actions on Haken manifolds with Heegaard genus two

Jungsoo Kim

paper

Handlebody-preserving finite group actions on Haken manifolds with Heegaard genus two

arXiv:0809.3624

Abstract

Let $M$ be a closed orientable 3-manifold with a genus two Heegaard splitting $(V_{1}, V_{2}; F)$ and a non-trivial JSJ-decomposition, where all components of the intersection of the JSJ-tori and $V_{i}$ are not $\partial$ -parallel in $V_{i}$ for $i = 1, 2$ . If $G$ is a finite group of orientation-preserving diffeomorphisms acting on $M$ which preserves each handlebody of the Heegaard splitting and each piece of the JSJ-decomposition of $M$ , then $G ≅ Z_{2}$ or $D_{2}$ if $V_{j} \cap (\cup T_{i})$ consists of at most two disks or at most two annuli.

arXiv comment22 pages, 13 figures, 2 tables