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Generic linear perturbations


Author: Shunsuke Ichiki
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 57R45, 58K25, 57R40
DOI: https://doi.org/10.1090/proc/14094
Published electronically: August 8, 2018
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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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Additional Information

Shunsuke Ichiki
Affiliation: Graduate School of Environment and Information Sciences, Yokohama National University, Yokohama 240-8501, Japan
Email: ichiki-shunsuke-jb@ynu.jp

DOI: https://doi.org/10.1090/proc/14094
Keywords: Generic linear perturbation, generic projection, stability, modular submanifold, transversality
Received by editor(s): June 23, 2017
Received by editor(s) in revised form: January 12, 2018
Published electronically: August 8, 2018
Additional Notes: The author is a Research Fellow PD of Japan Society for the Promotion of Science. The author is supported by JSPS KAKENHI Grant Number 16J06911.
Communicated by: Ken Ono
Article copyright: © Copyright 2018 American Mathematical Society

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