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.

Geometric equivalence among smooth map germs

Pages: 337 – 362



Shyuichi Izumiya (Department of Mathematics, Hokkaido University, Sapporo, Japan)

Masatomo Takahashi (Muroran Institute of Technology, Muroran, Japan)

Hiroshi Teramoto (Molecule & Life Nonlinear Science Laboratory, Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan)


We consider equivalence relations among smooth map germs with respect to geometry of $G$-structures on the target space germ. These equivalence relations are natural generalization of right-left equivalence (i.e., $\mathcal{A}$-equivalence) in the sense of Thom–Mather depending on geometric structures on the target space germ. Unfortunately, these equivalence relations are not necessarily geometric subgroups in the sense of Damon (1984). However, we have interesting applications of these equivalence relations.


$G$-structure, $\mathcal{A}$-equivalence, singularities of map germs

2010 Mathematics Subject Classification

Primary 58K40. Secondary 53C10.

This work is partially supported by Grant-in-Aid for Scientific Research (JSPS); (A) 26247006 (S.I), (C) 17K05238 (M.T) and JST PRESTO; JPMJPR16E8 (H.T).

Received 28 May 2018

Accepted 22 August 2019

Published 1 November 2019