Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 6, Number 4 (2006), 1831-1861.
Widths of surface knots
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.
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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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