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A note on braids and Parseval's theorem
Jonathan Fine
In 1988 Falk and Randell, based on Arnol'd's 1969 paper on braids, proved that the pure braid groups are residually nilpotent. They also proved that the quotients in the lower cent…
Vassiliev-Kontsevich invariants and Parseval's theorem
Jonathan Fine
We use an example to provide evidence for the statement: the Vassiliev-Kontsevich invariants of a knot (or braid) can be redefined so that . This c…
Some notes on the inverse problem for braids
Jonathan Fine
The Kontsevich integral associates to each braid (or more generally knot ) invariants lying in finite dimensional vector spaces, for . These v…
Vassiliev theory and regional change
Jonathan Fine
The purpose of this note is to state some definitions that may be useful in the study of knots, manifolds and the like. They apply to anything for which the concept of a regional c…