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Totoro
Totoro
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Let $M$ be a connected closed smooth manifold and $B(1)$ the unit ball in $\mathbb R^n$. Suppose $f:M \times B(1) \to M \times \mathbb R^n$ is a smooth embedding. 

Can we find an ambient isotopy $F_t$ of $M \times \mathbb R^n$ such that $F_0=\text{Id}$$F_0=\text{id} \times \text{id}$ and $F_1 \circ f=\text{Id}$?$F_1 \circ f=h\times \text{id}$, where $h$ is a self-diffeomorphism of $M$.

Let $M$ be a connected closed smooth manifold and $B(1)$ the unit ball in $\mathbb R^n$. Suppose $f:M \times B(1) \to M \times \mathbb R^n$ is a smooth embedding. Can we find an ambient isotopy $F_t$ of $M \times \mathbb R^n$ such that $F_0=\text{Id}$ and $F_1 \circ f=\text{Id}$?

Let $M$ be a connected closed smooth manifold and $B(1)$ the unit ball in $\mathbb R^n$. Suppose $f:M \times B(1) \to M \times \mathbb R^n$ is a smooth embedding. 

Can we find an ambient isotopy $F_t$ of $M \times \mathbb R^n$ such that $F_0=\text{id} \times \text{id}$ and $F_1 \circ f=h\times \text{id}$, where $h$ is a self-diffeomorphism of $M$.

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Totoro
Totoro
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  • 19

The existence of an isotopy in the manifold

Let $M$ be a connected closed smooth manifold and $B(1)$ the unit ball in $\mathbb R^n$. Suppose $f:M \times B(1) \to M \times \mathbb R^n$ is a smooth embedding. Can we find an ambient isotopy $F_t$ of $M \times \mathbb R^n$ such that $F_0=\text{Id}$ and $F_1 \circ f=\text{Id}$?