Quasi-isometry and Cohomology & Quan- tisation of Intervals

Thomas Gotfredsen

Research output: ThesisPh.D. thesis

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Abstract

This thesis covers the results from two projects.
In the frst project, we use a theorem of Koivisto, Kyed and Raum to show that a uniform measure equivalence between unimodular compactly generated locally compact second countable groups induces an isomorphism of their respective cohomologies, generalising a theorem of Sauer. We furthermore use this theorem to gain new insights on the quasi-isometry classification of simply connected nilpotent Lie groups, obtaining results which cannot be obtained using the previously well-known quasi-isometry classification results by Pansu, Shalom and Sauer. This project is joint work with David Kyed.
In the second project, we give a partial answer to a question posed by Aguilar and Kaad
on whether or not the standard Podle± quantum spheres converge to the 2-sphere as compact
quantum metric spaces. In particular, we show that its diagonal subalgebras, which are
equivalent to a family of quantised intervals, converge to the interval, and that they vary
continuously. This project is joint work with Jens Kaad and David Kyed.
Translated title of the contributionKvasiisometri og cohomologi & Kvantisering af intervaller
Original languageEnglish
Awarding Institution
  • University of Southern Denmark
Supervisors/Advisors
  • Kyed, David, Supervisor
Publisher
DOIs
Publication statusPublished - 19. Aug 2021

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