Generic linear perturbations

Abstract

In his celebrated paper "Generic projections", John Mather has shown that almost all linear projections from a submanifold of a vector space into a subspace are transverse with respect to a given modular submanifold. In this paper, an improvement of Mather's result is stated. Namely, we show that almost all linear perturbations of a smooth mapping from a submanifold of ${\mathbb{R}}^m$ into ${\mathbb{R}}^{\ell }$ yield a transverse mapping with respect to a given modular submanifold. Moreover, applications of this result are given.

11 pages, to appear in Proceedings of the American Mathematical Society

References in corpus (1)

• Recognizable classification of Lorentzian distance-squared mappings

Cited by in corpus (3)

• Stability of non-proper functions
• Whitney theorem for complex polynomial mappings
• Composing generic linearly perturbed mappings and immersions/injections