On an analogue of L2-Betti numbers for finite field coefficients and a question of Atiyah
by Johannes Neumann
Date of Examination:2016-07-06
Date of issue:2016-07-12
Advisor:Prof. Dr. Thomas Schick
Referee:Prof. Dr. Thomas Schick
Referee:Prof. Dr. Laurent Bartholdi
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Abstract
English
We construct a dimension function for modules over the group ring of an amenable group. This may replace the von Neumann dimension in the definition of L2-Betti numbers and thus allows an analogue definition for finite field coefficients. Furthermore we construct examples for characteristic 2 in answer to Atiyah question of irrational L2-Betti numbers.
Keywords: von Neumann dimension; amenable; group ring modules; dimension; finite characteristic; L2-Betti numbers; Atiyah Conjecture