The group Aut and Out of the fundamental group of a closed Sol 3-manifold

Daciberg Lima Gonçalves; Sérgio Tadao Martins

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arXiv · 1909.05292

The group Aut and Out of the fundamental group of a closed Sol 3-manifold

Daciberg Lima Gonçalves·Sérgio Tadao Martins

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Abstract

Let $E$ be the fundamental group of a closed Sol 3-manifold. We describe the groups $Aut(E)$ and $Out(E)$. We first consider the case where $E$ is the fundamental group of a torus bundle, and then the case where $E$ is the fundamental group of a closed Sol 3-manifold which is not a torus bundle. The groups are described in terms of some iterated semi-direct products of well known groups, where one exception is for $Out(E)$ for some $E$'s, in which case $Out(E)$ is described as an extension and a presentation is given.

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Daciberg Lima Gonçalves, Sérgio Tadao Martins. 2019-09-11. The group Aut and Out of the fundamental group of a closed Sol 3-manifold. https://arxiv.org/abs/1909.05292

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