Mixing
Whitney sum of smooth vector bundles
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I was reading through Lee's smooth manifolds book, in his chapter on vector bundles. Upon reading about smooth vector bundles and its definition, I was wondering if the whitney sum of two smooth vector bundles would be smooth, i.e. $p colon E oplus E' to M $ where $alpha colon E to M$ and $beta colon F to M$ are smooth vector bundles? How would one verify this, how is the direct sum of two smooth manifolds defined?
general-topology manifolds differential-topology
asked Oct 15 '14 at 23:33
chariot123chariot123
111
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I was reading through Lee's smooth manifolds book, in his chapter on vector bundles. Upon reading about smooth vector bundles and its definition, I was wondering if the whitney sum of two smooth vector bundles would be smooth, i.e. $p colon E oplus E' to M $ where $alpha colon E to M$ and $beta colon F to M$ are smooth vector bundles? How would one verify this, how is the direct sum of two smooth manifolds defined?
general-topology manifolds differential-topology
asked Oct 15 '14 at 23:33
chariot123chariot123
111
$endgroup$
add a comment |
$begingroup$
I was reading through Lee's smooth manifolds book, in his chapter on vector bundles. Upon reading about smooth vector bundles and its definition, I was wondering if the whitney sum of two smooth vector bundles would be smooth, i.e. $p colon E oplus E' to M $ where $alpha colon E to M$ and $beta colon F to M$ are smooth vector bundles? How would one verify this, how is the direct sum of two smooth manifolds defined?
general-topology manifolds differential-topology
asked Oct 15 '14 at 23:33
chariot123chariot123
111
$endgroup$
I was reading through Lee's smooth manifolds book, in his chapter on vector bundles. Upon reading about smooth vector bundles and its definition, I was wondering if the whitney sum of two smooth vector bundles would be smooth, i.e. $p colon E oplus E' to M $ where $alpha colon E to M$ and $beta colon F to M$ are smooth vector bundles? How would one verify this, how is the direct sum of two smooth manifolds defined?
general-topology manifolds differential-topology
general-topology manifolds differential-topology
asked Oct 15 '14 at 23:33
chariot123chariot123
111
asked Oct 15 '14 at 23:33
chariot123chariot123
111
asked Oct 15 '14 at 23:33
chariot123chariot123
111
asked Oct 15 '14 at 23:33
chariot123chariot123
111
asked Oct 15 '14 at 23:33
chariot123chariot123
111
111
add a comment |
add a comment |
1 Answer
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Yes, the Whitney sum of two smooth vector bundles is a smooth vector bundle. I guess you must be looking at the first edition of my book, which didn't mention Whitney sums. If you can get ahold of a copy of the second edition, this is proved in Example 10.7.
answered Oct 16 '14 at 5:00
Jack LeeJack Lee
27.4k54767
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$begingroup$
Yes, the Whitney sum of two smooth vector bundles is a smooth vector bundle. I guess you must be looking at the first edition of my book, which didn't mention Whitney sums. If you can get ahold of a copy of the second edition, this is proved in Example 10.7.
answered Oct 16 '14 at 5:00
Jack LeeJack Lee
27.4k54767
$endgroup$
add a comment |
$begingroup$
Yes, the Whitney sum of two smooth vector bundles is a smooth vector bundle. I guess you must be looking at the first edition of my book, which didn't mention Whitney sums. If you can get ahold of a copy of the second edition, this is proved in Example 10.7.
answered Oct 16 '14 at 5:00
Jack LeeJack Lee
27.4k54767
$endgroup$
add a comment |
$begingroup$
Yes, the Whitney sum of two smooth vector bundles is a smooth vector bundle. I guess you must be looking at the first edition of my book, which didn't mention Whitney sums. If you can get ahold of a copy of the second edition, this is proved in Example 10.7.
answered Oct 16 '14 at 5:00
Jack LeeJack Lee
27.4k54767
$endgroup$
Yes, the Whitney sum of two smooth vector bundles is a smooth vector bundle. I guess you must be looking at the first edition of my book, which didn't mention Whitney sums. If you can get ahold of a copy of the second edition, this is proved in Example 10.7.
answered Oct 16 '14 at 5:00
Jack LeeJack Lee
27.4k54767
answered Oct 16 '14 at 5:00
Jack LeeJack Lee
27.4k54767
answered Oct 16 '14 at 5:00
Jack LeeJack Lee
27.4k54767
answered Oct 16 '14 at 5:00
Jack LeeJack Lee
27.4k54767
27.4k54767
add a comment |
add a comment |
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