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Cihan
Cihan
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Let $M$ be a connected (topological) oriented $m$-manifold (say without boundary), and let $f \colon M \to M$ a homeomorphism$\operatorname{Homeo}^+(M)$ be the group of orientation preserving homeomorphisms $M \to M$. 

Is it true that for every $f \in \operatorname{Homeo}^+(M)$, there is a locally flat oriented embedding $\Phi \colon \mathbb{D}^m \hookrightarrow M$ and an orientation preserving homeomorphism $F \colon M \to M$$F \in \operatorname{Homeo}^+(M)$ such that $F$ is isotopic to $f$ and $F \Phi = \Phi$?

Let $M$ be a connected (topological) oriented $m$-manifold, and $f \colon M \to M$ a homeomorphism. Is there a locally flat oriented embedding $\Phi \colon \mathbb{D}^m \hookrightarrow M$ and an orientation preserving homeomorphism $F \colon M \to M$ such that $F$ is isotopic to $f$ and $F \Phi = \Phi$?

Let $M$ be a connected (topological) oriented $m$-manifold (say without boundary), and let $\operatorname{Homeo}^+(M)$ be the group of orientation preserving homeomorphisms $M \to M$. 

Is it true that for every $f \in \operatorname{Homeo}^+(M)$, there is a locally flat oriented embedding $\Phi \colon \mathbb{D}^m \hookrightarrow M$ and $F \in \operatorname{Homeo}^+(M)$ such that $F$ is isotopic to $f$ and $F \Phi = \Phi$?

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Cihan
Cihan
  • 1.7k
  • 11
  • 32

Can every orientation preserving homeomorphism of a manifold isotoped to be identity on a locally flat embedded disk?

Let $M$ be a connected (topological) oriented $m$-manifold, and $f \colon M \to M$ a homeomorphism. Is there a locally flat oriented embedding $\Phi \colon \mathbb{D}^m \hookrightarrow M$ and an orientation preserving homeomorphism $F \colon M \to M$ such that $F$ is isotopic to $f$ and $F \Phi = \Phi$?