Cusp equivalence between smooth embeddings of the 2-sphere in 4-space

Details Cusp equivalence between smooth embeddings of the 2-sphere in 4-space Cusp equivalence between smooth embeddings of the 2-sphere in 4-space

1999-11-20

arxiv.org/abs/math/9911257v1

Geom. Topol. Monogr. 2 (1999), 343-348

Mathematics

Geometric Topology

6 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper19.abs.html

Scientific paper

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.

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