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2 results

  • 12 - Higher Index Theory for Coarsely Embeddable Spaces

  • from Part Four - Higher Index Theory and Assembly
  • Rufus Willett, University of Hawaii, Manoa, Guoliang Yu, Texas A & M University
  • Book:
    Higher Index Theory
    Published online:
    11 June 2020
    Print publication:
    02 July 2020, pp 429-483

  • Summary

    Two types of counterexample to the coarse Baum-Connes conjecture: injectivity counterexamples coming from Dirac operators and positive scalar curvtaure on large spheres; and surjectivity counterexamples coming from spectral gap phenomena associated to expander graphs.Some general discussion of expander graphs, including constructions from property tau.

  • Property T and Amenable Transformation Group C*-algebras

  • F. Kamalov
  • Journal:
    Canadian Mathematical Bulletin / Volume 58 / Issue 1 / 01 March 2015
    Published online by Cambridge University Press:
    20 November 2018, pp. 110-114
    Print publication:
    01 March 2015
    • Article
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  • It is well known that a discrete group that is both amenable and has Kazhdan’s Property $T$ must be finite. In this note we generalize this statement to the case of transformation groups. We show that if $G$ is a discrete amenable group acting on a compact Hausdorff space $X$, then the transformation group ${{C}^{*}}$-algebra ${{C}^{*}}\left( X,\,G \right)$ has Property $T$ if and only if both $X$ and $G$ are finite. Our approach does not rely on the use of tracial states on ${{C}^{*}}\left( X,\,G \right)$.