Widths of surface knots

Takeda, Yasushi

doi:10.2140/agt.2006.6.1831

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Widths of surface knots

Yasushi Takeda

Algebraic & Geometric Topology 6 (2006) 1831–1861

DOI: 10.2140/agt.2006.6.1831

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

Volume 6, issue 4 (2006)