Classification of Artin groups admitting retractions onto their parabolic subgroups
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911519742099456 |
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| author | de la Cruz, Bruno Aarón Cisneros Cumplido, María Foniqi, Islam Paris, Luis |
| author_facet | de la Cruz, Bruno Aarón Cisneros Cumplido, María Foniqi, Islam Paris, Luis |
| contents | We classify the Artin groups that admit retractions onto all of their parabolic subgroups. Our approach relies on a detailed analysis of triangular subgroups, with a key ingredient being the classification of homomorphisms between dihedral Artin groups that map one of the standard generators to a standard generator. As a consequence, we show that whenever an Artin group admits retractions to parabolic subgroups, it also admits ordinary ones - that is, retractions that send each standard generator either to a standard generator or to the identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15314 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of Artin groups admitting retractions onto their parabolic subgroups de la Cruz, Bruno Aarón Cisneros Cumplido, María Foniqi, Islam Paris, Luis Group Theory 20F36 We classify the Artin groups that admit retractions onto all of their parabolic subgroups. Our approach relies on a detailed analysis of triangular subgroups, with a key ingredient being the classification of homomorphisms between dihedral Artin groups that map one of the standard generators to a standard generator. As a consequence, we show that whenever an Artin group admits retractions to parabolic subgroups, it also admits ordinary ones - that is, retractions that send each standard generator either to a standard generator or to the identity. |
| title | Classification of Artin groups admitting retractions onto their parabolic subgroups |
| topic | Group Theory 20F36 |
| url | https://arxiv.org/abs/2603.15314 |