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A new knot invariant. (English) Zbl 0632.57006
The author introduces a new knot invariant, based on Schubert’s bridge number, but which captures more of the complexity of the knot. This invariant is defined as follows. Given a smooth closed curve K embedded in $${\mathbb{R}}^ 3$$ and a line $$\delta$$ in $${\mathbb{R}}^ 3$$, the bridge number of K with respect to $$\delta$$ is the number of components of the critical set of the orthogonal projection from K to $$\delta$$. The author defines the superbridge number of K as the maximum of this bridge number when $$\delta$$ ranges over all directions in $${\mathbb{R}}^ 3$$. And the superbridge index of the knot [K] is the minimum of the superbridge number over all curves isotopic to K. The main result of the article is an explicit computation of the superbridge index of torus knots.
Reviewer: F.Bonahon

##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010)
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##### References:
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