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      Vassiliev invariants and knots modulo pure braid subgroups

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          Abstract

          We show that two knots have matching Vassiliev invariants of order less than n if and only if they are equivalent modulo the nth group of the lower central series of some pure braid group, thus characterizing Vassiliev's knot invariants in terms of the structure of the braid groups. We also prove some results about knots modulo the nth derived subgroups of the pure braid groups, and about knots modulo braid subgroups in general.

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          Most cited references14

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          On the Vassiliev knot invariants

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            Closed incompressible surfaces in alternating knot and link complements

            W. Menasco (1984)
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              A spanning tree expansion of the jones polynomial

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                Author and article information

                Journal
                20 May 1998
                Article
                math/9805092
                95cefa45-3354-40bf-a9bd-06d59dadcbd3
                History
                Custom metadata
                57M25
                21 pages, plain tex, 4 eps figures
                math.GT math.QA

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