Volume 6, issue 4 (2006)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Widths of surface knots

Yasushi Takeda

Algebraic & Geometric Topology 6 (2006) 1831–1861

arXiv: 0905.3488

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.

Keywords
Surface knot, bridge index, width, total width, braid index, spun knot, ribbon surface knot
Mathematical Subject Classification 2000
Primary: 57Q45
Secondary: 57M25
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Publication
Received: 7 February 2006
Revised: 10 August 2006
Accepted: 21 August 2006
Published: 1 November 2006
Authors
Yasushi Takeda
Graduate School of Mathematics
Kyushu University
Hakozaki
Fukuoka 812-8581
Japan