# On Turing machines, groupoids, and Atiyha problem

 dc.contributor.advisor Thom, Andreas Prof. Dr. de dc.contributor.author Grabowski, Łukasz de dc.date.accessioned 2011-03-17T12:11:50Z de dc.date.accessioned 2013-01-18T13:20:45Z de dc.date.available 2013-01-30T23:50:54Z de dc.date.issued 2011-03-17 de dc.identifier.uri http://hdl.handle.net/11858/00-1735-0000-0006-B6AB-5 de dc.identifier.uri http://dx.doi.org/10.53846/goediss-2479 dc.description.abstract Turing-dynamische Systeme, abstrakte Version von Turingmaschinen, werden mittels Gruppoide definiert und untersucht. Die wichtigste vorgelegte Anwendung betrifft das Atiyah-Problem. Zum Beispiel, wird bewiesen, dass jede nicht-negative reelle Zahl auch eine l2-Bettizahl ist. 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 On Turing machines, groupoids, and Atiyha problem de dc.type doctoralThesis de dc.title.translated Über Turingmaschinen, Gruppoide, und das Atiyah-problem de dc.contributor.referee Thom, Andreas Prof. Dr. de dc.date.examination 2011-03-10 de dc.description.abstracteng Turing dynamical system, an abstract version of a Turing machine, is defined and investigated using groupoids. The main presented application is to the Atiyah problem in group theory. It is for example proven that every non-negative real number is an l2-Betti number arising from some group. de dc.contributor.coReferee Schick, Thomas Prof. Dr. de dc.subject.ger Atiyah-problem de dc.subject.ger Atiayah-vermutung de dc.subject.ger Turingmaschine de dc.subject.ger dynamische Systeme de dc.subject.ger Bettizahlen de dc.subject.eng Atiyah problem de dc.subject.eng Atiyah conjecture de dc.subject.eng Turing machine de dc.subject.eng dynamical system de dc.subject.eng Betti numbers de dc.identifier.urn urn:nbn:de:gbv:7-webdoc-2884-4 de dc.identifier.purl webdoc-2884 de dc.affiliation.institute Fakultät für Mathematik und Informatik de dc.identifier.ppn 664122469 de
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