definition of top-form over \(C^\infty\) manifold with boundary
Topics
About: \(C^\infty\) manifold
The table of contents of this article
Starting Context
- The reader knows a definition of \(q\)-form over \(C^\infty\) manifold with boundary.
Target Context
- The reader will have a definition of top-form over \(C^\infty\) manifold with boundary.
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:
\( M\): \(\in \{\text{ the } d \text{ -dimensional } C^\infty \text{ manifolds with boundary } \}\)
\( (T^0_d (TM), M, \pi)\): \(= \text{ the } C^\infty (0, d) \text{ -tensors bundle over } M\)
\( (\Lambda_d (TM), M, \pi)\): \(= \text{ the } C^\infty d \text{ -covectors bundle over } M\)
\(*f\): \(: M \to T^0_d (TM)\) such that \(Ran (f) \subseteq \Lambda_d (TM)\) or \(: M \to \Lambda_d (TM)\), \(\in \{\text{ the sections }\}\)
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Conditions:
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2: Note
In short, 'top-form' is any \(d\)-form.
