Regular homotopy classes of singular maps

• Autores: András Juhász
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 90, Nº 3, 2005, págs. 738-762
• Idioma: inglés
• DOI: 10.1112/s0024611504015102
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• Resumen

  • Two locally generic maps $f, g \colon M^n \to \mathbb{R}^{2n - 1}$ are regularly homotopic if they lie in the same path-component of the space of locally generic maps. Our main result is that if $n \neq 3$ and $M^n$ is a closed $n$-manifold then the regular homotopy class of every locally generic map $f \colon M^n \to \mathbb{R}^{2n - 1}$ is completely determined by the number of its singular points provided that $f$ is singular (that is, $f$ is not an immersion).