Generic linear perturbations

Ichiki, Shunsuke

doi:10.1090/proc/14094

Generic linear perturbations
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Proc. Amer. Math. Soc. 146 (2018), 4981-4991 Request permission

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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