Algebraic & Geometric Topology

Widths of surface knots

Yasushi Takeda

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We study surface knots in 4–space by using generic planar projections. These projections have fold points and cusps as their singularities and the image of the singular point set divides the plane into several regions. The width (or the total width) of a surface knot is a numerical invariant related to the number of points in the inverse image of a point in each of the regions. We determine the widths of certain surface knots and characterize those surface knots with small total widths. Relation to the surface braid index is also studied.

Article information

Algebr. Geom. Topol., Volume 6, Number 4 (2006), 1831-1861.

Received: 7 February 2006
Revised: 10 August 2006
Accepted: 21 August 2006
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Surface knot bridge index width total width braid index spun knot ribbon surface knot


Takeda, Yasushi. Widths of surface knots. Algebr. Geom. Topol. 6 (2006), no. 4, 1831--1861. doi:10.2140/agt.2006.6.1831.

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