Hilbert class field - Revision history

en>R.e.b.: /* Examples */ Fixing style/layout errors

2015-01-11T18:12:16Z

Examples: Fixing style/layout errors

← Older revision		Revision as of 20:12, 11 January 2015
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	~~In [[mathematics]], '''K-homology'''~~ is ~~a [[homology (mathematics)\|homology]] theory on the [[Category (mathematics)\|category]] of locally [[compact space\|compact]] [[Hausdorff space]]s~~. ~~It classifies the elliptic [[pseudo-differential operator]]s acting on the [[vector bundle]]~~s ~~over a space~~. ~~In terms~~ of ~~[[C-algebra\|<math>C^</math>-algebras]], it classifies~~ the ~~[[Fredholm module]]~~s ~~over~~ an ~~[[algebra]]~~.		The writer is called Wilber Pegues. Alaska is exactly where he's usually been living. She is really fond of caving but she doesn't have the time recently. Office supervising is where her primary income arrives from but she's already utilized for an additional one.<br><br>Take a look at my web blog; online psychic readings ([http://afeen.fbho.net/v2/index.php?do=/profile-210/info/ please click for source])

	~~An '''operator [[homotopy]]''' between two Fredholm modules <math>(\mathcal{H},F_0,\Gamma)</math> and~~ <~~math~~>~~(\mathcal{H},F_1,\Gamma)~~<~~/math~~> is a ~~[[norm~~ (~~mathematics)\|norm]]~~ [~~[Continuous function\|continuous]] [[Path (topology)\|path]] of Fredholm modules, <math>t \mapsto (\mathcal{H},F_t,\Gamma)<~~/~~math>, <math>t \in [0,1]~~.~~</math> Two Fredholm modules are then equivalent if they are related by [[unitary transformation]]s or operator homotopies~~. ~~The <math>K^0(A)<~~/~~math> [[group (mathematics)\|group]] is the [[abelian group]] of [[equivalence relation\|equivalence classes]] of even Fredholm modules over A. The <math>K^1(A)<~~/~~math> group is the abelian group of equivalence classes of odd Fredholm modules over A~~. ~~Addition is given by [[Direct sum of modules\|direct summation]] of Fredholm modules, and the [[Inverse (mathematics)\|inverse]] of <math>(\mathcal{H}, F, \Gamma)<~~/~~math> is <math>(\mathcal{H},~~ -~~F, -\Gamma).<~~/~~math>~~

	~~== References ==~~
	* N. Higson and J. Roe, ''Analytic K-homology''. Oxford University Press, 2000.

	~~{{PlanetMath attribution\|id=3330\|title=K-homology}}~~

	~~[[Category:K-theory]~~]

en>Roentgenium111: /* Generalizations */ this could use an article (or at least mention in CFT article)

2013-06-18T01:06:44Z

Generalizations: this could use an article (or at least mention in CFT article)

← Older revision		Revision as of 03:06, 18 June 2013
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	[~~http://findyourflirt.net/index.php?m=member_profile&p=profile&id=117823 psychic love readings~~] ~~Andrew Berryhill~~ is ~~what his wife enjoys to call him and he completely digs that name. Office supervising is exactly where her primary income comes from but she'~~s ~~already applied for another one~~. It's ~~not~~ a ~~common factor but what she likes doing is to perform domino but she doesn't have~~ the ~~time recently~~. ~~For a while I~~'~~ve been in Mississippi but now~~ ~~tarot card readings~~ ([~~http:~~//~~chungmuroresidence~~.~~com~~/xe/~~reservation_branch2/152663 chungmuroresidence~~.~~com~~]) ~~I'm considering other options.~~<br><br>~~My webpage :: [http:~~/~~/kard~~.~~dk/?p~~=~~24252 online reader~~]		In [[mathematics]], '''K-homology''' is a [[homology (mathematics)\|homology]] theory on the [[Category (mathematics)\|category]] of locally [[compact space\|compact]] [[Hausdorff space]]s. It classifies the elliptic [[pseudo-differential operator]]s acting on the [[vector bundle]]s over a space. In terms of [[C-algebra\|<math>C^</math>-algebras]], it classifies the [[Fredholm module]]s over an [[algebra]].

			An '''operator [[homotopy]]''' between two Fredholm modules <math>(\mathcal{H},F_0,\Gamma)</math> and <math>(\mathcal{H},F_1,\Gamma)</math> is a [[norm (mathematics)\|norm]] [[Continuous function\|continuous]] [[Path (topology)\|path]] of Fredholm modules, <math>t \mapsto (\mathcal{H},F_t,\Gamma)</math>, <math>t \in [0,1].</math> Two Fredholm modules are then equivalent if they are related by [[unitary transformation]]s or operator homotopies. The <math>K^0(A)</math> [[group (mathematics)\|group]] is the [[abelian group]] of [[equivalence relation\|equivalence classes]] of even Fredholm modules over A. The <math>K^1(A)</math> group is the abelian group of equivalence classes of odd Fredholm modules over A. Addition is given by [[Direct sum of modules\|direct summation]] of Fredholm modules, and the [[Inverse (mathematics)\|inverse]] of <math>(\mathcal{H}, F, \Gamma)</math> is <math>(\mathcal{H}, -F, -\Gamma).</math>

			== References ==
			* N. Higson and J. Roe, ''Analytic K-homology''. Oxford University Press, 2000.

			{{PlanetMath attribution\|id=3330\|title=K-homology}}

			[[Category:K-theory]]

en>MathKnight: /* References */ +he:

2012-08-01T16:32:48Z

References: +he:

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