definition of \(C^\infty\) vectors bundle
Topics
About: \(C^\infty\) manifold
The table of contents of this article
Starting Context
- The reader knows a definition of \(C^\infty\) manifold with boundary.
- The reader knows a definition of \(C^\infty\) locally trivial surjection of rank \(k\).
Target Context
- The reader will have a definition of \(C^\infty\) vectors bundle.
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.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( M\): \(\in \{\text{ the } C^\infty \text{ manifolds with boundary }\}\)
\( E\): \(\in \{\text{ the } C^\infty \text{ manifolds with boundary }\}\)
\( k\): \(\in \mathbb{N} \setminus \{0\}\)
\( \pi\): \(: E \to T\), \(\in \{\text{ the } C^\infty \text{ locally trivial surjections of rank } k\}\)
\(*(E, M, \pi)\):
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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 \(C^\infty\) vectors bundle.
