Methods and Applications of Analysis

Volume 25 (2018)

Number 4

In Memory of Professor John N. Mather: Part 2 of 3

Guest Editors: Sen Hu, University of Science and Technology, China; Stanisław Janeczko, Polish Academy of Sciences, Poland; Stephen S.-T. Yau, Tsinghua University, China; and Huaiqing Zuo, Tsinghua University, China.

Transversality theorems on generic linearly perturbed mappings

Pages: 323 – 336



Shunsuke Ichiki (Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan)


In his celebrated paper “Generic projections”, John Mather has given a striking transversality theorem and its applications on generic projections. On the other hand, in this paper, two transversality theorems on generic linearly perturbed $C^r$ mappings are shown $(r \geq 1)$. Moreover, some applications of the two theorems are also given.


generic linear perturbation, transversality, immersion, injection

2010 Mathematics Subject Classification

57R42, 57R45

The author was supported by JSPS KAKENHI Grant Numbers JP16J06911 and JP19J00650.

Received 13 June 2018

Accepted 6 August 2018

Published 1 November 2019