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Comparison of perturbed Dirac operators

Authors: Jeffrey Fox and Peter Haskell
Journal: Proc. Amer. Math. Soc. 124 (1996), 1601-1608
MSC (1991): Primary 58G10
MathSciNet review: 1317036
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Abstract: This paper extends the index theory of perturbed Dirac operators to a collection of noncompact even-dimensional manifolds that includes both complete and incomplete examples. The index formulas are topological in nature. They can involve a compactly supported standard index form as well as a form associated with a Toeplitz pairing on a hypersurface.

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  • [A1] N. Anghel, An abstract index theorem on non-compact Riemannian manifolds, Houston J. Math. 19 (1993), 223--237. MR 94c:58193
  • [A2] N. Anghel, $L^{2}$-index formulae for perturbed Dirac operators, Commun. Math. Phys. 128 (1990), 77--97. MR 91b:58243
  • [BiC] J.-M. Bismut and J. Cheeger, $\eta $-invariants and their adiabatic limits, J. Amer. Math. Soc. 2 (1989), 33--70. MR 89k:58269
  • [B1] J. Brüning, $L^{2}$-index theorems on certain complete manifolds, J. Differential Geom. 32 (1990), 491--532. MR 91h:58103
  • [B2] J. Brüning, On $L^{2}$-index theorems for complete manifolds of rank-one type, Duke Math. J. 66 (1992), 257--309. MR 93i:58145
  • [BM] J. Brüning and H. Moscovici, $L^{2}$-index for certain Dirac-Schrödinger operators, Duke Math. J. 66 (1992), 311--336. MR 93g:58142
  • [BS1] J. Brüning and R. Seeley, An index theorem for first order regular singular operators, Am. J. Math. 110 (1988), 659--714. MR 89k:58271
  • [BS2] J. Brüning and R. Seeley, The resolvent expansion for second order regular singular operators, J. Funct. Anal. 73 (1987), 369--429. MR 88g:35151
  • [Bu] U. Bunke, On constructions making Dirac operators invertible at infinity, preprint, 1992.
  • [Ca] C. Callias, Axial anomalies and index theorems on open spaces, Commun. Math. Phys. 62 (1978), 213--234. MR 80h:58045a
  • [Cf] P. Chernoff, Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Anal. 12 (1973), 401--414. MR 51:6119
  • [FH] J. Fox and P. Haskell, Index theory for perturbed Dirac operators on manifolds with conical singularities, Proceedings of the Amer. Math. Soc. 123 (1995), 2265--2273. MR 95i:58172
  • [Ga] C. Gajdzinski, $L^{2}$-index for perturbed Dirac operator on odd dimensional open complete manifold, preprint, 1993.
  • [GLa] M. Gromov and H. B. Lawson, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. I.H.E.S. 58 (1983), 83--196. MR 85g:58082
  • [GuHi] E. Guentner and N. Higson, A note on Toeplitz operators, preprint, 1993.
  • [L] M. Lesch, Deficiency indices for symmetric Dirac operators on manifolds with conic singularities, Topology 32 (1993), 611--623. MR 94e:58133
  • [R] J. Råde, Callias' index theorem, elliptic boundary conditions, and cutting and gluing, Commun. Math. Phys. 161 (1994), 51--61. MR 95b:58143

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Additional Information

Jeffrey Fox
Affiliation: Mathematics Department, University of Colorado, Boulder, Colorado 80309

Peter Haskell
Affiliation: Mathematics Department, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

Keywords: Perturbed Dirac operator
Received by editor(s): October 24, 1994
Additional Notes: Jeffrey Fox’s work was supported by the National Science Foundation. \endgraf Peter Haskell’s work was supported by the National Science Foundation under Grant No. DMS-9204275.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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