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Markov classes in certain finite quotients of Artin’s braid group. (English) Zbl 0621.20025

Authors’ summary: This paper studies three finite quotients of the sequence of braid groups \(\{B_ n\); \(n=1,2,...\}\). Each has the property that Markov classes in \(B_{\infty}=\amalg B_ n\) pass to well-defined equivalence classes in the quotient. We are able to solve the Markov problem in two of the quotients, obtaining canonical representatives for Markov classes and giving a procedure for reducing an arbitrary representative to the canonical one. The results are interpreted geometrically, and related to link invariants of the associated links and the value of the Jones polynomial [V. Jones, Bull. Am. Math. Soc., New. Ser. 12, 103-111 (1985; Zbl 0564.57006)] on the corresponding classes.
Reviewer: S.C.Althoen

MSC:

20F36 Braid groups; Artin groups
20F65 Geometric group theory
57M25 Knots and links in the \(3\)-sphere (MSC2010)

Citations:

Zbl 0564.57006
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References:

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