Braid Notation

Stepan Orevkov determined the braid index and found minimum width braid representatives for most of the links in LinkInfo. Lower bounds for the braid index were found using the Morton-Franks-Williams Inequality based on the Jones polynomial. In a few cases, this inequality was applied to the link with its components doubled, replacing each component with two parallel components. Computations were done using a program written by Morton and Short. Upper bounds were found be building explicit braid representatives; most of these could be done using [5]. The remaining cases were handled by using basic techniques to simplify given braid representatives.


[1] Orevkov, Stepan, Personal communication.