Translator Disclaimer
July, 2018 Composing generic linearly perturbed mappings and immersions/injections
Shunsuke ICHIKI
J. Math. Soc. Japan 70(3): 1165-1184 (July, 2018). DOI: 10.2969/jmsj/77237723

Abstract

Let $N$ (resp., $U$) be a manifold (resp., an open subset of ${\mathbb{R}}^m$). Let $f:N\to U$ and $F:U\to {\mathbb{R}}^\ell$ be an immersion and a $C^{\infty}$ mapping, respectively. Generally, the composition $F\circ f$ does not necessarily yield a mapping transverse to a given subfiber-bundle of $J^1(N,\mathbb{R}^\ell)$. Nevertheless, in this paper, for any $\mathcal{A}^1$-invariant fiber, we show that composing generic linearly perturbed mappings of $F$ and the given immersion $f$ yields a mapping transverse to the subfiber-bundle of $J^1(N,\mathbb{R}^\ell)$ with the given fiber. Moreover, we show a specialized transversality theorem on crossings of compositions of generic linearly perturbed mappings of a given mapping $F:U\to \mathbb{R}^\ell$ and a given injection $f:N\to U$. Furthermore, applications of the two main theorems are given.

Funding Statement

The author was supported by JSPS KAKENHI Grant Number 16J06911.

Citation

Download Citation

Shunsuke ICHIKI. "Composing generic linearly perturbed mappings and immersions/injections." J. Math. Soc. Japan 70 (3) 1165 - 1184, July, 2018. https://doi.org/10.2969/jmsj/77237723

Information

Received: 30 January 2017; Published: July, 2018
First available in Project Euclid: 12 June 2018

zbMATH: 06966979
MathSciNet: MR3830804
Digital Object Identifier: 10.2969/jmsj/77237723

Subjects:
Primary: 57R45
Secondary: 57R42

Rights: Copyright © 2018 Mathematical Society of Japan

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.70 • No. 3 • July, 2018
Back to Top