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

Takao Matumoto

Geometry & Topology Monographs 2 (1999) 343–348

DOI: 10.2140/gtm.1999.2.343

arXiv: math.GT/9911257

Abstract

If the fundamental group of the complement of a smooth embedding f:S2R4 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 S2R4; cusp equivalence, stable equivalence and weakly stable equivalence.

Keywords

cusp, generic deformation of maps, smooth 2–knots, stable equivalence

Mathematical Subject Classification

Primary: 57Q45

Secondary: 57R45

References
Publication

Received: 30 December 1998
Revised: 12 April 1999
Published: 20 November 1999

Authors
Takao Matumoto
Department of Mathematics
Faculty of Science
Hiroshima University
Higashi-Hiroshima 739-8526
Japan