Relationships between braid length and the number of braid strands

Details Relationships between braid length and the number of braid strands Relationships between braid length and the number of braid strands

2006-05-17

arxiv.org/abs/math/0605476v2

Mathematics

Geometric Topology

9 pages, 2 figures; minor revisions

Scientific paper

For a knot K, let b_n(K) be the minimum length of an n-stranded braid representative of K. Examples of knots exist for which b_n(K) is a non-increasing function. We investigate the behavior of b_n(K). We develop bounds on the function in terms of the genus of K, with stronger results for homogeneous knots and braid positive knots. For knots of nine or fewer crossings, we show that b_n(K) is an increasing function and determine it completely.

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