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arXiv · 1804.10853

Critical points and surjectivity of smooth maps

Yongjie Shi·Chengjie Yu
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Abstract

Let $f:M^m\to N^n$ be a smooth map between two differential manifolds with $N$ connected, $f(M)$ closed and $f(M)\neq N$. In this short note, we show that either all the points of $M$ are critical points of $f$ or the dimension the collection of all critical points of $f$ is not less than $n-1$. Some consequences of this result for surjectivity of mappings are also presented.

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Yongjie Shi, Chengjie Yu. 2018-04-28. Critical points and surjectivity of smooth maps. https://arxiv.org/abs/1804.10853

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