Coarse Geometry for Noncommutative Spaces

by Tathagata Banerjee
Doctoral thesis
Date of Examination:2015-11-25
Date of issue:2016-11-23
Advisor:Prof. Dr. Ralf Meyer
Referee:Prof. Dr. Ralf Meyer
Referee:Prof. Dr. Thomas Schick
Persistent Address: http://dx.doi.org/10.53846/goediss-5996

 

 

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Abstract

English

We develop an analogoue of coarse geometry for noncommutative spaces in terms of unitizations of the given C* -algebra. Examples for our theory come from Rieffel deformation of compactifications under strongly continuous actions of R^d. A special case of this is the coarse structure on the Moyal plane, seen as a Rieffel deformation of the classical plane. The motivating question for this project has been to investigate a possible coarse equivalence between the classical plane and the Moyal plane, which seems plausible in physics. We define a noncommutative analogue of coarse maps. Our definition ensures that the classical and the Moyal plane with their standard coarse structures are coarsely equivalent. A more general result holds for Rieffel deformations of arbitrary actions of R^d by translations.
Keywords: C*-algebra; Coarse structure; Compactification; Rieffel deformation
 
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