The isomorphism problem for large-type Artin groups
| Autor: | Vaskou, Nicolas |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper we solve the isomorphism problem for all large-type Artin groups. Our strategy involves reconstructing the Coxeter groups associated with large-type Artin groups in a purely algebraic way. This answers several questions raised by Charney. We also study 2-dimensional Artin groups in general. By classifying all their dihedral Artin subgroups, we are able to give strong results of rigidity for all 2-dimensional Artin groups. We prove that "most" standard generators in 2-dimensional Artin groups are preserved under isomorphisms (up to conjugation). We also show that an isomorphism between large-type Artin groups preserves the set of spherical parabolic subgroups if and only if the defining graphs do not have even-labelled leaves. Finally, we show that Artin groups whose defining graphs have even-labelled leaves are never co-Hopfian. Comment: 73 pages, 19 figures. In this new version we completely solve the isomorphism problem for all large-type Artin groups. We also extend many of our results to all 2-dimensional Artin groups. There are many new additional results. This paper is the first part of a longer paper that was split. The second paper is now called "Automorphisms of large-type free-of-infinity Artin groups" |
| Databáze: | arXiv |
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