## Tokyo Journal of Mathematics

### Whitney's Umbrellas in Stable Perturbations of a Map Germ $({\bf R}^n, 0)\to ({\bf R}^{2n- 1}, 0)$

Mariko OHSUMI

#### Abstract

Let $f:({\bf R}^n, 0)\to ({\bf R}^p, 0)$ be a $C^{\infty}$ map-germ. We are interested in whether the number modulo 2 of stable singular points of codimension $n$ that appear near the origin in a generic perturbation of $f$ is a topological invariant. In this paper we concentrate on investigating the problem when $p$ is $2n- 1$, where stable singular points of codimension $n$ are only Whitney's umbrellas, and give a positive answer to the problem.

#### Article information

Source
Tokyo J. Math., Volume 29, Number 2 (2006), 475-493.

Dates
First available in Project Euclid: 1 February 2007

https://projecteuclid.org/euclid.tjm/1170348180

Digital Object Identifier
doi:10.3836/tjm/1170348180

Mathematical Reviews number (MathSciNet)
MR2284985

Zentralblatt MATH identifier
1135.58016

#### Citation

OHSUMI, Mariko. Whitney's Umbrellas in Stable Perturbations of a Map Germ $({\bf R}^n, 0)\to ({\bf R}^{2n- 1}, 0)$. Tokyo J. Math. 29 (2006), no. 2, 475--493. doi:10.3836/tjm/1170348180. https://projecteuclid.org/euclid.tjm/1170348180

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