Algebraic & Geometric Topology

Widths of surface knots

Yasushi Takeda

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796607

Digital Object Identifier
doi:10.2140/agt.2006.6.1831

Mathematical Reviews number (MathSciNet)
MR2263051

Zentralblatt MATH identifier
1132.57021

Subjects
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}

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

Citation

Takeda, Yasushi. Widths of surface knots. Algebr. Geom. Topol. 6 (2006), no. 4, 1831--1861. doi:10.2140/agt.2006.6.1831. https://projecteuclid.org/euclid.agt/1513796607


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