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Book Information

Author(s): Calvin C. Moore and Claude Schochet
Title: Global analysis on foliated spaces
Additional book information: Mathematical Sciences Research Institute Publications, vol. 9, Springer-Verlag, New York, Berlin, Heidelberg, 1988, 377 pp., $34.00. ISBN 0-387-96664-1

[ABP] M. F. Atiyah, R. Bott, and V. K. Patodi, On the heat equation and the index theorem, Invent. Math. 19 (1973), 279-330. MR 650828

[AS] M. F. Atiyah and I. M. Singer, The index of elliptic operators. I, Ann. of Math. (2) 87(1968), 484-530. MR 236950

[BV] N. Berline and M. Vergne, A proof of Bismut local index theorem for a family of Dirac operators, Topology 26 (1987), 435-464. MR 919729

[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 813584

[D] H. Donnelly, Local index theorem for families, Michigan Math. J. 35 (1988), 11-20. MR 931936

[Gz] E. Getzler, A short proof of the local Atiyah-Singer index theorem, Topology 25 (1986), 111-117. MR 836727

[G1] P. B. Gilkey, Invariance theory, the heat equation, and the Atiyah-Singer index theorem, Publish or Perish, Inc., 1984. MR 783634

[G2] P. B. Gilkey, Curvature and the eigenvalues of the Laplacianfor elliptic complexes, Adv. in Math. 10 (1973), 344-381. MR 324731

[HL] J. L. Heitsch and C. Lazarov, A Lefschetz theorem for foliated manifolds, preprint. MR 1056266

[MP] S. Minakshisundaram and A. Pleijel, Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242-256. MR 31145

[P] R. Palais, Seminar on the Atiyah-Singer index theorem, Ann. of Math. Study no. 57, Princeton Univ. Press, Princeton, N. J., 1965. MR 198494

[Pt] V. K. Patodi, Curvature and the eigenforms of the Laplace operator, J. Differential Geom. 5(1971), 233-249. MR 292114

[R1] J. Roe, An index theorem on open manifolds, J. Differential Geom. 27 (1988), 87-113. MR 918459

[R2] J. Roe, Finite propagation speed and Connes'foliation algebra, Proc. Cambridge Philos. Soc. 102 (1987), 459-466. MR 906620

[S] R. T. Seeley, Complex powers of an elliptic operator, Proc. Sympos. Pure Math., vol. 10, Amer. Math. Soc., Providence, R. I., 1967, pp. 288-307. MR 237943

Review Information:
Journal: Bull. Amer. Math. Soc. 20 (1989), 112-117.
DOI: 10.1090/S0273-0979-1989-15720-0
PII: S 0273-0979(1989)15720-0

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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