Lagrange mappings of the first open Whitney umbrella

I.A. Bogaevski and G. Ishikawa

Vol. 203 (2002), No. 1, 115–138

DOI: 10.2140/pjm.2002.203.115

Abstract

In this paper we give a classification of simple stable singularities of Lagrange projections of the first open Whitney umbrella, the simplest singularity of Lagrange varieties. Our classification extends the ADE-classification, due to Arnold, of simple stable singularities of Lagrange projections of smooth Lagrange submanifolds. We also prove a criterion of equivalence of stable Lagrange projections of open Whitney umbrellas which is analogous to Mather’s fundamental theorem on stable map-germs.

Milestones

Received: 16 May 2000

Revised: 1 February 2001

Published: 1 March 2002