The Eta Invariant and Families of Pseudodifferential Operators

@inproceedings{Melrose1995TheEI,
  title={The Eta Invariant and Families of Pseudodifferential Operators},
  author={Richard B. Melrose},
  year={1995}
}
For a compact manifold without boundary a suspended algebra of pseudodifferential operators is considered; it is an algebra of pseudodifferential operators on, and translation-invariant in, an additional real variable. It is shown that the eta invariant, as defined by Atiyah, Patodi and Singer for admissible Dirac operators, extends to a homomorphism from the ring of invertible elements of the suspended algebra to the additive real line. The deformation properties of this extended eta… CONTINUE READING