Widths of surface knots

Details Widths of surface knots Widths of surface knots

2009-05-21

arxiv.org/abs/0905.3488v1

Algebr. Geom. Topol. 6 (2006) 1831-1861

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 1 November 2006

Scientific paper

10.2140/agt.2006.6.1831

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.

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