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

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

2008-09-22

arxiv.org/abs/0809.3624v4

Mathematics

Geometric Topology

22 pages, 13 figures, 2 tables

Scientific paper

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 $G\cong \mathbb{Z}_2$ or $\mathbb{D}_2$ if $V_j\cap(\cup T_i)$ consists of at most two disks or at most two annuli.

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