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Zhiqiang
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Let $\Sigma$ be a closed surface smoothly embedded in $\mathbb R^3$. For any smoothMorse function $h:\mathbb R^3 \to \mathbb R$, can we isotope $\Sigma$ so that the restriction of $h$ on $\Sigma$ is also a Morse function?

Let $\Sigma$ be a closed surface smoothly embedded in $\mathbb R^3$. For any smooth function $h:\mathbb R^3 \to \mathbb R$, can we isotope $\Sigma$ so that the restriction of $h$ on $\Sigma$ is a Morse function?

Let $\Sigma$ be a closed surface smoothly embedded in $\mathbb R^3$. For any Morse function $h:\mathbb R^3 \to \mathbb R$, can we isotope $\Sigma$ so that the restriction of $h$ on $\Sigma$ is also a Morse function?

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Zhiqiang
  • 891
  • 3
  • 11

Restriction function as a Morse function

Let $\Sigma$ be a closed surface smoothly embedded in $\mathbb R^3$. For any smooth function $h:\mathbb R^3 \to \mathbb R$, can we isotope $\Sigma$ so that the restriction of $h$ on $\Sigma$ is a Morse function?