Abstract
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 {ie160-1} = ∐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 on the corresponding classes.
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This material is based upon work partially supported by the National Science Foundation under Grant No. DMS-8503758.
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Birman, J.S., Wajnryb, B. Markov classes in certain finite quotients of artin’s braid group. Israel J. Math. 56, 160–178 (1986). https://doi.org/10.1007/BF02766122
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DOI: https://doi.org/10.1007/BF02766122