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  Helly meets Garside and Artin

Huang, J., & Osajda, D. (2021). Helly meets Garside and Artin. Inventiones Mathematicae, 225(2), 395-426. doi:10.1007/s00222-021-01030-8.

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 Urheber:
Huang, Jingyin1, Autor           
Osajda, Damian, Autor
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Schlagwörter: Mathematics, Group Theory, Algebraic Topology, Geometric Topology
 Zusammenfassung: A graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty intersection. We show that weak Garside groups of finite type and FC-type Artin groups are Helly, that is, they act geometrically on Helly graphs. In particular, such groups act geometrically on spaces with convex geodesic bicombing, equipping them with a nonpositive-curvature-like structure. That structure has many properties of a CAT(0) structure and, additionally, it has a combinatorial flavor implying biautomaticity. As immediate consequences we obtain new results for FC-type Artin groups (in particular braid groups and spherical Artin groups) and weak Garside groups, including e.g.\ fundamental
groups of the complements of complexified finite simplicial arrangements of hyperplanes, braid groups of well-generated complex reflection groups, and one-relator groups with non-trivial center. Among the results are: biautomaticity, existence of EZ and Tits boundaries, the Farrell-Jones
conjecture, the coarse Baum-Connes conjecture, and a description of higher
order homological and homotopical Dehn functions. As a mean of proving the
Helly property we introduce and use the notion of a (generalized) cell Helly
complex.

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Sprache(n): eng - English
 Datum: 2021
 Publikationsstatus: Erschienen
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 Ort, Verlag, Ausgabe: -
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 Art der Begutachtung: Expertenbegutachtung
 Identifikatoren: arXiv: 1904.09060
DOI: 10.1007/s00222-021-01030-8
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Titel: Inventiones Mathematicae
  Kurztitel : Invent. Math.
Genre der Quelle: Zeitschrift
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Affiliations:
Ort, Verlag, Ausgabe: Springer
Seiten: - Band / Heft: 225 (2) Artikelnummer: - Start- / Endseite: 395 - 426 Identifikator: -