Generic linear perturbations

Shunsuke Ichiki

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arXiv · 1607.03220

Generic linear perturbations

Shunsuke Ichiki

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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.

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Shunsuke Ichiki. 2016-07-12. Generic linear perturbations. https://arxiv.org/abs/1607.03220

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