Reversibility in the Seifert-fibered spaces
Abstract
An element $a$ in a group $\Gamma$ is called \emph{reversible} if there exists $g \in \Gamma$ such that $gag^{-1}=a^{-1}$. The reversible elements are also known as `real elements' or `reciprocal elements' in literature. In this paper, we classify the reversible elements in Fuchsian groups, and use this classification to find all reversible elements in a Seifert-fibered group. In the last section we apply this classification to the braid groups, particularly to the braid group on $3$ strands.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2024
- DOI:
- 10.48550/arXiv.2403.01541
- arXiv:
- arXiv:2403.01541
- Bibcode:
- 2024arXiv240301541D
- Keywords:
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- Mathematics - Geometric Topology;
- Primary 57K;
- Secondary 20H10;
- 20H05