Approximation of center-valued Betti-numbers and the center-valued Atiyah-conjecture

Knebusch, Anselm

dc.contributor.advisor	Schick, Thomas Prof. Dr.	de
dc.contributor.author	Knebusch, Anselm	de
dc.date.accessioned	2013-01-22T15:48:47Z	de
dc.date.available	2013-01-30T23:50:59Z	de
dc.date.issued	2009-11-25	de
dc.identifier.uri	http://hdl.handle.net/11858/00-1735-0000-000D-F16D-2	de
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-3475
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-3475
dc.description.abstract	In der Dissertation erweitern wir das Approximations-Theorem für Betti-Zahlen, von Lück, auf zentrums-wertige Betti-Zahlen. Dies erlaubt die vollständige Klassifizierung von L^2-Homologie-Moduln von G-KW-Komplexen durch ihre endlich dimensionalen Analoga. Im zweiten Teil beweisen wir eine zentrums-werige Erweiterung der Atiyah-Vermutung für elementar amenable Gruppen und benutzen das Approximations-Resultat um den Satz auf bestimmte Limes Gruppen auszudehnen.	de
dc.format.mimetype	application/pdf	de
dc.language.iso	eng	de
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/	de
dc.title	Approximation of center-valued Betti-numbers and the center-valued Atiyah-conjecture	de
dc.type	doctoralThesis	de
dc.title.translated	Approximation of center-valued Betti-numbers and the center-valued Atiyah-conjecture	de
dc.contributor.referee	Schick, Thomas Prof. Dr.	de
dc.date.examination	2009-10-19	de
dc.subject.dnb	510 Mathematik	de
dc.subject.gok	EEGL 000 Selfadjoint operator algebras	de
dc.subject.gok	EEGM 200 Methods of algebraic topology	de
dc.description.abstracteng	In the Thesis, we extend Lück"s approximation theorem for Betti-numbers to center-valued Betti-numbers. This allows to classify homology modules of G-CW complexes by looking at there finite dimensional analogues. In the second part we proof a center-valued version of the Atiyah-conjecture for elementary amenable groups, and use the approximation theorem to extend it to certain limit groups, e.g. pure braid groups.	de
dc.contributor.coReferee	Vaes, Stefaan Prof. Dr.	de
dc.subject.topic	Mathematics and Natural Science	de
dc.subject.ger	Betti-Zahlen	de
dc.subject.ger	von Neumann-Algebren	de
dc.subject.ger	Operatortheorie	de
dc.subject.ger	G-CW-Komplex	de
dc.subject.ger	Approximation	de
dc.subject.ger	Atiyah Vermutung	de
dc.subject.eng	Betti-numbers	de
dc.subject.eng	von Neumann-algebras	de
dc.subject.eng	operatortheory	de
dc.subject.eng	G-CW-complex	de
dc.subject.eng	approximation	de
dc.subject.eng	Atiyah conjecture	de
dc.subject.bk	31.55 Globale Analysis	de
dc.subject.bk	31.47 Operatortheorie	de
dc.identifier.urn	urn:nbn:de:gbv:7-webdoc-2261-3	de
dc.identifier.purl	webdoc-2261	de
dc.identifier.ppn	633133086	de

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