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Book Review
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Book Information
Author(s):
N. Berline, E. Getzler and M. Vergne
Title:
Heat kernels and Dirac operators
Additional book information:
Grundlehren Math. Wiss., vol. 298,
Springer-Verlag, New York,
1992,
vii + 369,
$79.00,
ISBN 3-540-53340-0
References:
- At
- M. Atiyah, Collected Works, Vols.
 and  , Clarendon Press, Oxford, 1988, MR 91h:01094c; MR 91h:01094d. - ABP
- M. Atiyah, R. Bott and V.K. Patodi, On the heat equation and the index theorem, Invent. Math. 19 (1973), 279-330. MR 58:31287; MR 58:31288.
- APS
- M. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Camb. Phil. Soc. 77 (1975), 43-69, MR 53:1655a.
- AS1
- M. Atiyah and I.M. Singer, The index of elliptic operators on compact manifolds, Bull. Amer. Math. Soc. 69 (1963), 422-433, MR 28:626.
- AS2
- ------, The index of elliptic operators, I, Ann. Math. 87 (1968), 484-530, MR 38:5243.
- B
- J.-M. Bismut, The Atiyah-Singer index theorem for families of Dirac operators; two heat equation proofs, Invent. Math. 83 (1986), 91-151, MR 87g:58117.
- CM
- A. Connes and H. Moscovici, The local index formula in noncommutative geometry, Preprint.
- Ge
- E. Getzler, Pseudodifferential operators on supermanifolds and the index theorem, Comm. Math. Phys. 92 (1983), 163-178, MR 86a:58104.
- Gi
- P. Gilkey, Curvature and the eigenvalues of the Dolbeault complex for Kaehler manifolds, Adv. in Math. 11 (1973), 311-325, MR 48:12609.
- LM
- B. Lawson and M.-L. Michelsohn, Spin Geometry, Princeton Math Series No. 38, Princeton Univ. Press, Princeton, 1989, MR 91g:53001.
- McS
- H. McKean and I.M. Singer, Curvature and the eigenvalues of the Laplacian, J. Diff. Geom. 1 (1967), 43-69, MR 36:828.
- Pa
- R.S. Palais, ed., Seminar on the Atiyah-Singer index theorem, Annals of Math. Study No. 57, Princeton Univ. Press, Princeton, 1965, MR 33:6649.
- R
- J. Roe, Elliptic operators, topology and asymptotic methods, Pitman Res. Notes in Math. Series, vol. 179, Longman Scientific and Technical, Harlow, 1988, MR 89j:58126.
- V
- M. Vergne, Formule de Kirillov et indice de l'opérateur de Dirac, Proceedings of the International Congress of Mathematicians, Warszawa 1983, PWN, Warszawa, and North-Holland, Amsterdam, New York, Oxford, 1984, pp. (921-934), MR 87d:22022.
Additional Information:
Reviewer(s):
Rafe
Mazzeo
Affiliation:
Stanford University
Email:
mazzeo@math.stanford.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
33
(1996),
125-129.
DOI:
10.1090/S0273-0979-96-00633-7
PII:
S 0273-0979(96)00633-7
Copyright of article:
Copyright
1996,
American Mathematical Society
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