Geometry & Topology Monographs 2 (1999),
Proceedings of the Kirbyfest,
paper no. 19, pages 343-348.
Cusp equivalence between smooth embeddings of the 2-sphere in 4-space
If the fundamental group of the complement of a smooth embedding f:
S^2 \subset R^4 is a cyclic group, the map can be deformed to the
standard embedding by a generic one-parameter family with at most cusp
singularities. If two smooth embeddings are connected by such a
deformation, they will be called cusp equivalent. We will discuss the
relation of three equivalences of smooth 2-knots S^2 \subset R^4; cusp
equivalence, stable equivalence and weakly stable equivalence.
Cusp, generic deformation of maps, smooth 2-knots, stable equivalence
AMS subject classification.
Primary: 57Q45. Secondary: 57R45.
Submitted: 30 December 1998.
(Revised: 12 April 1999.)
Published: 20 November 1999.
Notes on file formats
Department of Mathematics, Faculty of Science, Hiroshima University
Higashi-Hiroshima 739-8526, Japan
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