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Pré-Publication, Document De Travail Année : 2023

Endomorphisms of Artin groups of type D

Résumé

In this paper we determine a classification of the endomorphisms of the Artin group of type $D_n$ for $n\ge 6$. In particular we determine its automorphism group and its outer automorphism group. We also determine a classification of the homomorphisms from the Artin group of type $D_n$ to the Artin group of type $A_{n-1}$ and a classification of the homomorphisms from the Artin group of type $A_{n-1} $ to the Artin group of type $D_n$ for $n\ge 6$. The results are algebraic in nature but the proofs are based on topological arguments (curves on surfaces and mapping class groups).
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Dates et versions

hal-04152823 , version 1 (05-07-2023)
hal-04152823 , version 2 (28-08-2023)
hal-04152823 , version 3 (04-03-2024)
hal-04152823 , version 4 (21-05-2024)

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Fabrice Castel, Luis Paris. Endomorphisms of Artin groups of type D. 2023. ⟨hal-04152823v1⟩
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