Deciding whether a mapping torus is of full rank

Juemin Lin; Jianchun Wu

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arXiv · 2306.07602

Deciding whether a mapping torus is of full rank

Juemin Lin·Jianchun Wu

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Abstract

The mapping torus induced by an automorphism $\phi$ of the free abelian group $\mathbb{Z}^n$ is a semi-direct product $G=\mathbb{Z}^n\rtimes_\phi \mathbb{Z}$. We show that whether the rank of $G$ is equal to $n+1$ is decidable. As a corollary, the rank of $\mathbb{Z}^3\rtimes_\phi \mathbb{Z}$ is decidable.

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Juemin Lin, Jianchun Wu. 2023-06-13. Deciding whether a mapping torus is of full rank. https://arxiv.org/abs/2306.07602

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