Tokyo Journal of Mathematics

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


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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.

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

First available in Project Euclid: 1 February 2007

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Zentralblatt MATH identifier

Primary: 32S30: Deformations of singularities; vanishing cycles [See also 14B07] 32S50: Topological aspects: Lefschetz theorems, topological classification, invariants 58C25: Differentiable maps
Secondary: 58K15: Topological properties of mappings 58K60: Deformation of singularities 58K65: Topological invariants


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.

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