A fixed point theorem on noncompact manifolds

  title={A fixed point theorem on noncompact manifolds},
  author={P. Hochs and Hang Wang},
  journal={arXiv: K-Theory and Homology},
  • P. Hochs, Hang Wang
  • Published 2015
  • Mathematics
  • arXiv: K-Theory and Homology
  • We generalise the Atiyah-Segal-Singer fixed point theorem to noncompact manifolds. Using $KK$-theory, we extend the equivariant index to the noncompact setting, and obtain a fixed point formula for it. The fixed point formula is the explicit cohomological expression from Atiyah-Segal-Singer's result. In the noncompact case, however, we show in examples that this expression yields characters of infinite-dimensional representations. In one example, we realise characters of discrete series… CONTINUE READING
    3 Citations
    Orbital integrals and $K$-theory classes
    • 4
    • PDF


    Index theorem for equivariant Dirac operators on non-compact manifolds
    • 58
    • Highly Influential
    • PDF
    Geometric quantization and families of inner products
    • 28
    • PDF
    Heat Kernels and Dirac Operators
    • 1,745
    • PDF