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regular homotopy

Proceedings of the London Mathematical Society (1)

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Regular homotopy classes of singular maps
András Juhász
Journal:

Proceedings of the London Mathematical Society / Volume 90 / Issue 3 / May 2005

Published online by Cambridge University Press:

22 April 2005, pp. 738-762

Print publication:

May 2005
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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).