Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1175115578, G121809054, G143639328, G1855990336, G2262748287, G2281333282, G2309174360, G2390397592, G2585926585, G2659019386, G2660406951, G279363373, G300979063, G34346518, G3480869486, Categories, Geometry, Braids, G425668148, G430777504, G5080475149, G5421974903, G586857820, Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité, G6448809991, G6803667113, G7084143925, G7391727506, Algorithmic, topological and geometric aspects of infinite groups, monoids and inverse semigroups, G846842501, G8920660035, G897484643, G99296377
OpenAlex ID: W7138243716