Relative hyperbolicity and Artin groups

Ilya Kapovich; Paul Schupp

doi:10.1007/s10711-004-9285-0

Relative hyperbolicity and Artin groups

Ilya Kapovich
, Paul Schupp

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let G = 〈a₁,...,a_n|a_ia _ja_i...= a_ja_ia_j,...,i < j∠ be an Artin group and let m_ij = m_ji be the length of each of the sides of the defining relation involving a_i and a_j. We show if all m_ij ≥ 7 then G is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups 〈a_i, a_j〉 for which m_ij < ∞.

Original language	English (US)
Pages (from-to)	153-167
Number of pages	15
Journal	Geometriae Dedicata
Volume	107
Issue number	1
DOIs	https://doi.org/10.1007/s10711-004-9285-0
State	Published - 2004

Keywords

Artin groups
Relatively hyperbolic

ASJC Scopus subject areas

Geometry and Topology

Online availability

10.1007/s10711-004-9285-0

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abstract = "Let G = 〈a1,...,an|aia jai...= ajaiaj,...,i < j∠ be an Artin group and let mij = mji be the length of each of the sides of the defining relation involving ai and aj. We show if all mij ≥ 7 then G is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups 〈ai, aj〉 for which mij < ∞.",

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AB - Let G = 〈a1,...,an|aia jai...= ajaiaj,...,i < j∠ be an Artin group and let mij = mji be the length of each of the sides of the defining relation involving ai and aj. We show if all mij ≥ 7 then G is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups 〈ai, aj〉 for which mij < ∞.

KW - Artin groups

KW - Relatively hyperbolic

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Relative hyperbolicity and Artin groups

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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