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Mathematics > Group Theory

arXiv:math/0703692 (math)
[Submitted on 23 Mar 2007 (v1), last revised 19 Apr 2007 (this version, v2)]

Title:Representations of Braid Groups and Generalisations

Authors:Valerij G. Bardakov (AOSSI), Paolo Bellingeri (LMJL)
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Abstract: We define and study extensions of Artin's representation and braid monodromy representation to the case of topological and algebraical generalisations of braid groups. In particular we provide faithful representations of braid groups of oriented surfaces with boundary components as (outer) automorphisms of free groups. We give also similar representations for braid groups of non oriented surfaces with boundary components and we show a representation of braid groups of closed surfaces as outer automorphisms of free groups. Finally, we provide faithful representations of Artin-Tits groups of type $\mathcal{D}$ as automorphisms of free groups.
Comments: Few misprints corrected, simpler proof for proposition 10
Subjects: Group Theory (math.GR)
MSC classes: Primary 20F36; Secondary 20F05, 20F10
Cite as: arXiv:math/0703692 [math.GR]
  (or arXiv:math/0703692v2 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.math/0703692

Submission history

From: Paolo Bellingeri [view email]
[v1] Fri, 23 Mar 2007 10:18:59 UTC (19 KB)
[v2] Thu, 19 Apr 2007 12:01:26 UTC (19 KB)
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