New York Journal of Mathematics
Volume 11 (2005) 303-332

  

Jeffrey Fox and Peter Haskell

The Atiyah-Patodi-Singer theorem for perturbed Dirac operators on even-dimensional manifolds with bounded geometry


Published: June 30, 2005
Keywords: Atiyah-Patodi-Singer theorem, eta invariant, perturbed Dirac operator, heat expansion
Subject: 58J20, 58J28, 58J32, 58J35

Abstract
This paper establishes conditions under which one can prove an Atiyah-Patodi-Singer index theorem for perturbed Dirac operators on complete noncompact even-dimensional manifolds with boundary. This index theorem introduces into index theory spectral invariants of self-adjoint perturbed Dirac operators on noncompact manifolds.

Acknowledgements

Jeffrey Fox's work was supported by the National Science Foundation. Peter Haskell's work was supported by the National Science Foundation under Grant No. DMS-9800782.


Author information

Jeffrey Fox:
Mathematics Department, University of Colorado, Boulder, CO 80309-0395
jfox@euclid.colorado.edu

Peter Haskell:
Mathematics Department, Virginia Tech, Blacksburg, VA 24061-0123
haskell@math.vt.edu