Bulletin of the American Mathematical Society

MathSciNet review: 1567734
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Book Information:

Authors: 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.

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 and I. M. Singer, The index of elliptic operators. I, Ann. of Math. (2) 87 (1968), 484–530. MR 236950, DOI 10.2307/1970715

Nicole Berline and Michèle Vergne, A proof of Bismut local index theorem for a family of Dirac operators, Topology 26 (1987), no. 4, 435–463. MR 919729, DOI 10.1016/0040-9383(87)90041-3

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

Harold Donnelly, Local index theorem for families, Michigan Math. J. 35 (1988), no. 1, 11–20. MR 931936, DOI 10.1307/mmj/1029003678

Ezra Getzler, A short proof of the local Atiyah-Singer index theorem, Topology 25 (1986), no. 1, 111–117. MR 836727, DOI 10.1016/0040-9383(86)90008-X

Peter B. Gilkey, Invariance theory, the heat equation, and the Atiyah-Singer index theorem, Mathematics Lecture Series, vol. 11, Publish or Perish, Inc., Wilmington, DE, 1984. MR 783634

Peter B. Gilkey, Curvature and the eigenvalues of the Laplacian for elliptic complexes, Advances in Math. 10 (1973), 344–382. MR 324731, DOI 10.1016/0001-8708(73)90119-9

James L. Heitsch and Connor Lazarov, A Lefschetz theorem for foliated manifolds, Topology 29 (1990), no. 2, 127–162. MR 1056266, DOI 10.1016/0040-9383(90)90004-4

S. Minakshisundaram and Å. Pleijel, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242–256. MR 31145, DOI 10.4153/cjm-1949-021-5

Richard S. Palais, Seminar on the Atiyah-Singer index theorem, Annals of Mathematics Studies, No. 57, Princeton University Press, Princeton, N.J., 1965. With contributions by M. F. Atiyah, A. Borel, E. E. Floyd, R. T. Seeley, W. Shih and R. Solovay. MR 0198494

V. K. Patodi, Curvature and the eigenforms of the Laplace operator, J. Differential Geometry 5 (1971), 233–249. MR 292114

John Roe, An index theorem on open manifolds. I, II, J. Differential Geom. 27 (1988), no. 1, 87–113, 115–136. MR 918459

John Roe, Finite propagation speed and Connes’ foliation algebra, Math. Proc. Cambridge Philos. Soc. 102 (1987), no. 3, 459–466. MR 906620, DOI 10.1017/S0305004100067517

R. T. Seeley, Complex powers of an elliptic operator, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) Amer. Math. Soc., Providence, R.I., 1967, pp. 288–307. MR 0237943

[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 0650828




[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