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2 results

  • Spectral Flow Argument Localizing an Odd Index Pairing

  • Part of
  • Terry A. Loring, Hermann Schulz-Baldes
  • Journal:
    Canadian Mathematical Bulletin / Volume 62 / Issue 2 / June 2019
    Published online by Cambridge University Press:
    07 January 2019, pp. 373-381
    Print publication:
    June 2019
    • Article
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  • An odd Fredholm module for a given invertible operator on a Hilbert space is specified by an unbounded so-called Dirac operator with compact resolvent and bounded commutator with the given invertible. Associated with this is an index pairing in terms of a Fredholm operator with Noether index. Here it is shown by a spectral flow argument how this index can be calculated as the signature of a finite dimensional matrix called the spectral localizer.

  • Fibre product approach to index pairings for the generic Hopf fibration of SUq(2)

  • Elmar Wagner
  • Journal:
    Journal of K-Theory / Volume 7 / Issue 1 / February 2011
    Published online by Cambridge University Press:
    15 March 2010, pp. 1-17
    Print publication:
    February 2011

  • A fibre product construction is used to give a description of quantum line bundles over the generic Podlés spheres obtained by gluing two quantum discs along their boundaries. Representatives of the corresponding K0-classes are given in terms of 1-dimensional projections belonging to the C*-algebra, and in terms of analogues of the classical Bott projections. The K0-classes of quantum line bundles derived from the generic Hopf fibration of quantum SU(2) are determined and the index pairing is computed. It is argued that taking the projections obtained from the fibre product construction yields a significant simplification of earlier index computations.