Vassiliev invariants and knots modulo pure braid subgroups

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 pro...

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Bibliographic Details
Published in:arXiv.org 1998-05
Main Author: Stanford, Theodore B
Format: Article
Language:English
Subjects:
Braid theory
Invariants
Knots
Subgroups
Online Access:Get full text
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Summary: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.
ISSN:2331-8422