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Ludwik
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How to formalize this isotopy?

I'm estudying the H-Cobordism theorem following the Lectures of John Milnor, and in the proof of the Whitney trick for cancel pairs of self-intersection points I have the next problem with an isotopy wich is used without formal definition:

Considering the next plane model composed of two curves $C_0$ and $C'_0$ wich intersect transversally at two points $a$ and $b$ and enclose a disk $D$ in a domain $U$ of $\mathbb{R}^2$.

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Milnor says the following:

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What is the best way to formalize this isotopy?

Ludwik
  • 237
  • 1
  • 5