Widths of surface knots

Takeda, Yasushi¹

¹Graduate School of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan

Algebraic and Geometric Topology, Tome 6 (2006) no. 4, pp. 1831-1861

Résumé

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.

Détail

DOI : 10.2140/agt.2006.6.1831

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

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