Book Review
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Book Information:
Authors:
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 pp.,
ISBN 3-540-53340-0,
$79.00$
M. Atiyah, R. Bott, and V. K. Patodi, On the heat equation and the index theorem, Invent. Math. 19 (1973), 279–330. MR 650828, DOI 10.1007/BF01425417
M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43–69. MR 397797, DOI 10.1017/S0305004100049410
M. F. Atiyah and I. M. Singer, The index of elliptic operators. I, Ann. of Math. (2) 87 (1968), 484–530. MR 236950, DOI 10.2307/1970715
Jean-Michel Bismut, The Atiyah-Singer index theorem for families of Dirac operators: two heat equation proofs, Invent. Math. 83 (1986), no. 1, 91–151. MR 813584, DOI 10.1007/BF01388755
Ezra Getzler, Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem, Comm. Math. Phys. 92 (1983), no. 2, 163–178. MR 728863
H. Blaine Lawson Jr. and Marie-Louise Michelsohn, Spin geometry, Princeton Mathematical Series, vol. 38, Princeton University Press, Princeton, NJ, 1989. MR 1031992
John Roe, Elliptic operators, topology and asymptotic methods, Pitman Research Notes in Mathematics Series, vol. 179, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1988. MR 960889
Michèle Vergne, Formule de Kirillov et indice de l’opérateur de Dirac, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 921–934 (French). MR 804746
- 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.
Review Information:
Reviewer:
Rafe Mazzeo
Affiliation:
Stanford University
Email:
mazzeo@math.stanford.edu
Journal:
Bull. Amer. Math. Soc.
33 (1996), 125-129
DOI:
https://doi.org/10.1090/S0273-0979-96-00633-7
Review copyright:
© Copyright 1996
American Mathematical Society
