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Generic Projections in the Semi-nice Dimensions

Published online by Cambridge University Press:  04 December 2007

A. A. Du Plessis
Affiliation:
Matematisk Institut, Aarhus Universitet, Ny Munkegade, DK-8000 AarhusC, Denmark
C. T. C. Wall
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom
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Abstract

In his celebrated paper ‘Generic Projections’, Mather obtained the key result that a generic projection to an affine subspace of a smooth submanifold in Euclidean space is jet-transverse to any ‘modular’ submanifold of (multi-) jet space. He also gave an explicit stratification by modular submanifolds, and used it to conclude that the projection, if in the nice dimensions, is generically (C-) stable. In this article, we extend the result to the semi-nice dimensions (where only C0-stability is obtained), using the stratification given in our book. We first recall the definitions of the nice and semi-nice dimensions, review the main known results which involve them, and proceed to the statement of our main results. Next we discuss the condition of modularity, and present a number of methods for establishing modularity of particular strata. Finally, we show that all the strata needed for the main result are covered by these methods.

Type
Research Article
Copyright
© 2003 Kluwer Academic Publishers

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