Sheaf of connection algebras - Revision history

Vipul: 2 revisions

2008-05-18T20:09:10Z

2 revisions

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Vipul at 20:53, 6 April 2008

2008-04-06T20:53:05Z

← Older revision		Revision as of 20:53, 6 April 2008
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	==Definition==		==Definition==

	Let <math>M</math> be a [[differential manifold]] ~~and <math>E</math> a [[vector bundle]] over <math>M</math>~~. The '''sheaf of connection algebras''' of <math>E</math> is defined as follows:		Let <math>M</math> be a [[differential manifold]]. The '''sheaf of connection algebras''' of <math>M</math> is defined as follows:

	* For every open subset <math>U</math> of <math>M</math>, the object associated to <math>E</math> is the [[connection algebra]] associated to ~~the restriction of~~ <math>E</math> to a ~~vector bundle over <math>U</math>~~		* For every open subset <math>U</math> of <math>M</math>, the object associated to <math>U</math> is the [[connection algebra]] associated to <math>U</math>, viewed as a manifold.
	* The restriction map is defined ~~as follows: {{fillin}}~~		* The restriction map is defined using the natural restriction map for the [[sheaf of first-order differential operators]], and the [[sheaf of infinitely differentiable functions]]

	Sometimes the '''sheaf of connection algebras''' is termed the connection algebra, though the latter term is sometimes used for the ''global object''.		Sometimes the '''sheaf of connection algebras''' is termed the connection algebra, though the latter term is sometimes used for the ''global object''.

Vipul: New page: {{global analog|connection algebra}} ==Definition== Let $M$ be a differential manifold and $E$ a vector bundle over $M$ . The '''sheaf of connecti...

2008-04-06T20:50:42Z

New page: {{global analog|connection algebra}} ==Definition== Let <math>M</math> be a differential manifold and <math>E</math> a vector bundle over <math>M</math>. The '''sheaf of connecti...

New page

{{global analog|connection algebra}}

==Definition==

Let <math>M</math> be a [[differential manifold]] and <math>E</math> a [[vector bundle]] over <math>M</math>. The '''sheaf of connection algebras''' of <math>E</math> is defined as follows:

* For every open subset <math>U</math> of <math>M</math>, the object associated to <math>E</math> is the [[connection algebra]] associated to the restriction of <math>E</math> to a vector bundle over <math>U</math>
* The restriction map is defined as follows: {{fillin}}

Sometimes the '''sheaf of connection algebras''' is termed the connection algebra, though the latter term is sometimes used for the ''global object''.

Sheaf of connection algebras - Revision history

Vipul: 2 revisions

Vipul at 20:53, 6 April 2008

Vipul: New page: {{global analog|connection algebra}} ==Definition== Let M be a differential manifold and E a vector bundle over M. The '''sheaf of connecti...

Vipul: New page: {{global analog|connection algebra}} ==Definition== Let $M$ be a differential manifold and $E$ a vector bundle over $M$ . The '''sheaf of connecti...