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Topological Graph Theory

Graphs Session #4 #1

Subevent of Graphs Session #4

Central Time (US & Canada)

Starts at: 2025-08-13 08:30AM

Ends at: 2025-08-13 08:55AM

Flowers of knots

Kouki Taniyama ⟨taniyama@waseda.jp⟩

Abstract:

An (n,k)-flower F(n,k) is the shadow of the closure of an n-braid (σ1σ2σn1)k.
C. Lamm and V. O. Manturov independently showed the following: Let K be a knot and nbraid(K). Then K has F(n,k) as its shadow for some k. We show the following: Let K be a knot and kbridge(K). Then K has F(n,k) as its shadow for some n. As a corollary, we show bridge(K)=lr(K) where lr(K) is the left-right number of K. This gives us a new definition of the bridge number of a knot.

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