Presentations of Dehn quandles

Presentations of Dehn quandles

The paper gives two approaches to write explicit presentations for the class of Dehn quandles using presentations of their underlying groups. The first approach gives finite presentations for Dehn quandles of a class of Garside groups and Gaussian groups. The second approach is for general Dehn quan...

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Veröffentlicht in:arXiv.org 2022-02
Hauptverfasser: Dhanwani, Neeraj K, Raundal, Hitesh, Singh, Mahender
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Sprache:eng
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Mathematics - Geometric Topology
Mathematics - Group Theory
Mathematics - Quantum Algebra
Oil field equipment
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description The paper gives two approaches to write explicit presentations for the class of Dehn quandles using presentations of their underlying groups. The first approach gives finite presentations for Dehn quandles of a class of Garside groups and Gaussian groups. The second approach is for general Dehn quandles when the centralisers of generators of their underlying groups are known. Several examples including Dehn quandles of spherical Artin groups, surface groups and mapping class groups of orientable surfaces are given to illustrate the results.
doi_str_mv 10.48550/arxiv.2202.02531
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subjects Mathematics - Geometric Topology
Mathematics - Group Theory
Mathematics - Quantum Algebra
Oil field equipment
title Presentations of Dehn quandles
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