Parabolic subgroups acting on the additional length graph
| dc.contributor.author | Antolín Pichel, Yago | |
| dc.contributor.author | Cumplido, María | |
| dc.date.accessioned | 2023-06-17T09:20:24Z | |
| dc.date.available | 2023-06-17T09:20:24Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | Let A ≠ A1;A2;I2m be an irreducible Artin–Tits group of spherical type. We show that the periodic elements of A and the elements preserving some parabolic subgroup of A act elliptically on the additional length graph CAL(A), a hyperbolic, infinite diameter graph associated to A constructed by Calvez and Wiest to show that A/Z(A) is acylindrically hyperbolic. We use these results to find an element g ∈ A such that <P,g> ≅ P * <g> for every proper standard parabolic subgroup P of A. The length of g is uniformly bounded with respect to the Garside generators, independently of A. This allows us to show that, in contrast with the Artin generators case, the sequence ω(An,S)(with n ∈ N) of exponential growth rates of braid groups, with respect to the Garside generating set, goes to infinity. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación (MICINN) | |
| dc.description.sponsorship | Ministerio de Economía y Competitividad (MINECO) | |
| dc.description.sponsorship | Junta de Andalucía | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/69511 | |
| dc.identifier.doi | 10.2140/agt.2021.21.1791 | |
| dc.identifier.issn | 1472-2747 | |
| dc.identifier.officialurl | https://doi.org/10.2140/agt.2021.21.1791 | |
| dc.identifier.relatedurl | https://msp.org/agt/2021/21-4/p06.xhtml | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/8624 | |
| dc.issue.number | 4 | |
| dc.journal.title | Algebraic & Geometric Topology | |
| dc.language.iso | eng | |
| dc.page.final | 1816 | |
| dc.page.initial | 1791 | |
| dc.publisher | Mathematical Sciences Publishers (MSP) | |
| dc.relation.projectID | MTM2014-53810; SEV-2015-0554; MTM2016-76453-C2-1-P | |
| dc.relation.projectID | MTM2017-82690-P | |
| dc.relation.projectID | FQM-2018 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 512.54 | |
| dc.subject.keyword | Braid groups | |
| dc.subject.keyword | Artin groups | |
| dc.subject.keyword | Geometric group theory | |
| dc.subject.ucm | Álgebra | |
| dc.subject.ucm | Grupos (Matemáticas) | |
| dc.subject.unesco | 1201 Álgebra | |
| dc.title | Parabolic subgroups acting on the additional length graph | |
| dc.type | journal article | |
| dc.volume.number | 21 | |
| dcterms.references | [1] E Artin, Theory of braids, Ann. of Math. 48 (1947) 101–126 MR Zbl [2] M Bestvina, K Fujiwara, Bounded cohomology of subgroups of mapping class groups, Geom. Topol. 6 (2002) 69–89 MR Zbl [3] E Brieskorn, K Saito, Artin-Gruppen und Coxeter-Gruppen, Invent. Math. 17 (1972) 245–271 MR Zbl [4] M Calvez, B Wiest, Acylindrical hyperbolicity and Artin–Tits groups of spherical type, Geom. Dedicata 191 (2017) 199–215 MR Zbl [5] M Calvez, B Wiest, Curve graphs and Garside groups, Geom. Dedicata 188 (2017) 195–213 MR Zbl [6] M Calvez, B Wiest, Hyperbolic structures for Artin–Tits groups of spherical type, preprint (2019) arXiv To appear in Contemp. Math. [7] H S M Coxeter, The complete enumeration of finite groups of the form r2i=(ri,rj)kij=1, J. Lond. Math. Soc. 10 (1935) 21–25 Zbl [8] M Cumplido, On the minimal positive standardizer of a parabolic subgroup of an Artin–Tits group, J. Algebraic Combin. 49 (2019) 337–359 MR Zbl [9] M Cumplido, V Gebhardt, J González-Meneses, B Wiest, On parabolic subgroups of Artin–Tits groups of spherical type, Adv. Math. 352 (2019) 572–610 MR Zbl [10] F Dahmani, V Guirardel, D Osin, Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces, Mem. Amer. Math. Soc. 1156, Amer. Math. Soc., Providence, RI (2017) MR Zbl [11] P Dehornoy, L Paris, Gaussian groups and Garside groups, two generalisations of Artin groups, Proc. Lond. Math. Soc. 79 (1999) 569–604 MR Zbl [12] P Deligne, Les immeubles des groupes de tresses généralisés, Invent. Math. 17 (1972) 273–302 MR Zbl [13] T Delzant, Sous-groupes à deux générateurs des groupes hyperboliques, from “Group theory from a geometrical viewpoint” (É Ghys, A Haefliger, A Verjovsky, editors), World Sci., River Edge, NJ (1991) 177–189 MR Zbl [14] R Flores, J González-Meneses, On the growth of Artin–Tits monoids and the partial theta function, preprint (2018) arXiv [15] E Godelle, Normalisateurs et centralisateurs des sous-groupes paraboliques dans les groupes d’Artin–Tits, PhD thesis, Université de Picardie Jules Verne (2001) [16] E Godelle, Normalisateur et groupe d’Artin de type sphérique, J. Algebra 269 (2003) 263–274 MR Zbl [17] E Godelle, Parabolic subgroups of Garside groups, J. Algebra 317 (2007) 1–16 MR Zbl [18] P de la Harpe, Topics in geometric group theory, Univ. Chicago Press (2000) MR Zbl [19] H van der Lek, The homotopy type of complex hyperplane complements, PhD thesis, Katholieke Universiteit Nijmegen (1983) [20] L Paris, Parabolic subgroups of Artin groups, J. Algebra 196 (1997) 369–399 MR Zbl [21] L Paris, Artin monoids inject in their groups, Comment. Math. Helv. 77 (2002) 609–637 MR Zbl | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | bd3bab81-47d2-4551-811a-af8ac40597c5 | |
| relation.isAuthorOfPublication.latestForDiscovery | bd3bab81-47d2-4551-811a-af8ac40597c5 |
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