Singularities of the projections of surfaces in 4-space

Vera Carrara, J. Scott Carter and Masahico Saito

Vol. 199 (2001), No. 1, 21–40

DOI: 10.2140/pjm.2001.199.21

Abstract

We study the singularities of maps of surfaces from a knot theoretic point of view. We define and study colors and signs of branch and triple points on knotted surface projections and give formulas among the numbers of these. We prove that cusps can be canceled on the planar projections of knotted surfaces. For orientable knotted surfaces, we prove that both cusps and branch points can be canceled.

Milestones

Received: 1 December 1997

Revised: 30 October 1998

Published: 1 May 2001