5: C∞ Vectors Bundle

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definition of $C^{\mathrm{\infty }}$ vectors bundle

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Topics

About: $C^{\mathrm{\infty }}$ manifold

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Note

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Starting Context

• The reader knows a definition of $C^{\mathrm{\infty }}$ manifold with boundary.
• The reader knows a definition of $C^{\mathrm{\infty }}$ locally trivial surjection of rank $k$.

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Target Context

• The reader will have a definition of $C^{\mathrm{\infty }}$ vectors bundle.

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Orientation

There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$M$: $\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ manifolds with boundary }\}$
$E$: $\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ manifolds with boundary }\}$
$k$: $\in \mathbb{N}\setminus \{0\}$
$\pi$: $:E\to T$, $\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ locally trivial surjections of rank }k\}$
$\ast (E,M,\pi )$:
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Conditions:
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2: Note

This definition does not means that a $\pi$ exists for any arbitrary $M$ and $E$; it means that if a $\pi$ exists, $(E,M,\pi )$ is a $C^{\mathrm{\infty }}$ vectors bundle.

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References

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