On Turing machines, groupoids, and Atiyha problem

Über Turingmaschinen, Gruppoide, und das Atiyah-problem

by Łukasz Grabowski
Doctoral thesis
Date of Examination:2011-03-10
Date of issue:2011-03-17
Advisor:Prof. Dr. Andreas Thom
Referee:Prof. Dr. Andreas Thom
Referee:Prof. Dr. Thomas Schick
Persistent Address: http://dx.doi.org/10.53846/goediss-2479

 

 

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Abstract

English

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.
Keywords: Atiyah problem; Atiyah conjecture; Turing machine; dynamical system; Betti numbers

Other Languages

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.
Schlagwörter: Atiyah-problem; Atiayah-vermutung; Turingmaschine; dynamische Systeme; Bettizahlen
 
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