ABSTRACT

We apply the work in the previous chapter to the problem of what knots have a braided surface of minimal genus on the minimal number of strands. With the notation of §2.9, let σ i, k ∈ B n for 1 ≤ i < k ≤ n be the bands we introduced in (5.13): σ i , k : = σ i … σ k − 2 σ k − 1 σ k − 2 − 1 … σ i − 1 . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315368672/0420dd25-c037-4c97-970e-748b38aaf586/content/eq351.tif"/>