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Complexes of parabolic subgroups for Artin groups

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Virtualconference
Authors : Cumplido Cabello, Maria (Author of the conference)
CIRM (Publisher )

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Abstract : One of the main examples of Artin groups are braid groups. We can use powerful topological methods on braid groups that come from the action of braid on the curve complex of the n-puctured disk. However, these methods cannot be applied in general to Artin groups. In this talk we explain how we can construct a complex for Artin groups, which is an analogue to the curve complex in the braid case, by using parabolic subgroups.

Keywords : braid groups; Artin groups; simplicial complexes; parabolic subgroups

MSC Codes :
20F36 - Braid groups; Artin groups
20F65 - Geometric group theory
57M07 - Topological methods in group theory

Additional resources :
https://conferences.cirm-math.fr/uploads/1/6/6/4/16648158/cumplido_luminyvirtual.pdf

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 01/06/2020
    Conference Date : 22/05/2020
    Subseries : Research talks
    arXiv category : Group Theory ; Geometric Topology
    Mathematical Area(s) : Topology ; Algebra
    Format : MP4 (.mp4) - HD
    Video Time : 00:27:12
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/ 2020-05-22_Cumplido.mp4

Information on the Event

Event Title : Virtual Geometric Group Theory conference / Rencontre virtuelle en géométrie des groupes
Event Organizers : Chatterji, Indira ; Paris, Luis ; Vogtmann, Karen
Dates : 01/06/2020 - 05/06/2020
Event Year : 2020
Event URL : https://conferences.cirm-math.fr/virtual...

Citation Data

DOI : 10.24350/CIRM.V.19635803
Cite this video as: Cumplido Cabello, Maria (2020). Complexes of parabolic subgroups for Artin groups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19635803
URI : http://dx.doi.org/10.24350/CIRM.V.19635803

See Also

Bibliography

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  • CALVEZ, Matthieu, DE LA CRUZ, Bruno A. Cisneros, et CUMPLIDO, María. Conjugacy stability of parabolic subgroups of Artin-Tits groups of spherical type. Journal of Algebra, 2020. - https://doi.org/10.1016/j.jalgebra.2020.03.017

  • CALVEZ, Matthieu et DE LA CRUZ, Bruno A. Cisneros. Curve graphs for Artin-Tits groups of type $ B $, $\widetilde A $ and $\widetilde C $ are hyperbolic. arXiv preprint arXiv:2003.04796, 2020. - https://arxiv.org/abs/2003.04796

  • CALVEZ, Matthieu et WIEST, Bert. Hyperbolic structures for Artin-Tits groups of spherical type. arXiv preprint arXiv:1904.02234, 2019. - https://arxiv.org/abs/1904.02234

  • CHARNEY, Ruth et PARIS, Luis. Convexity of parabolic subgroups in Artin groups. Bull. of the London Math. Soc., 2014. - https://doi.org/10.1112/blms/bdu077

  • CUMPLIDO, María, GEBHARDT, Volker, GONZÁLEZ-MENESES, Juan, et al. On parabolic subgroups of Artin–Tits groups of spherical type. Advances in Mathematics, 2019, vol. 352, p. 572-610. - https://doi.org/10.1016/j.aim.2019.06.010

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  • GODELLE, Eddy. Normalisateur et groupe d'Artin de type sphérique. Journal of Algebra, 2003, vol. 269, no 1, p. 263-274. - https://doi.org/10.1016/S0021-8693(03)00529-5

  • GONZÁLEZ-MENESES, Juan. Geometric embeddings of braid groups do not merge conjugacy classes. Boletín de la Sociedad Matemática Mexicana, 2014, vol. 20, no 2, p. 297-305. - https://doi.org/10.1007/s40590-014-0018-6

  • MORRIS-WRIGHT, Rose. Parabolic subgroups of Artin groups of FC type. arXiv preprint arXiv:1906.07058, 2019. - https://arxiv.org/abs/1906.07058

  • PARIS, Luis. Parabolic subgroups of Artin groups. Journal of Algebra, 1997, vol. 196, no 2, p. 369-399. - https://doi.org/10.1006/jabr.1997.7098



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