Journal of Differential Geometry

The adiabatic limit, Hodge cohomology and Leray's spectral sequence for a fibration

Rafe R. Mazzeo and Richard B. Melrose

Full-text: Open access

Article information

J. Differential Geom., Volume 31, Number 1 (1990), 185-213.

First available in Project Euclid: 26 June 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58A14: Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]
Secondary: 55R20: Spectral sequences and homology of fiber spaces [See also 55Txx] 58G15


Mazzeo, Rafe R.; Melrose, Richard B. The adiabatic limit, Hodge cohomology and Leray's spectral sequence for a fibration. J. Differential Geom. 31 (1990), no. 1, 185--213. doi:10.4310/jdg/1214444094.

Export citation


  • [1] J.-M. Bismut, Mecanique aleatoire, Lecture Notes in Math., Vol. 866, Springer, Berlin, 1981.
  • [2] J.-M. Bismut and J. Cheeger, Invariants et a et indices des families pour les varietesa. bord, C. R. Acad. Sci. Paris 305 (1987) 127-130.
  • [3] J.-M. Bismut and D. S. Freed, The analysis of elliptic families, I. Metrics and connections on determinant bundles, Comm. Math. Phys. 106 (1986) 159-176; II.Dirac operators, Eta invariants and the holonomy theorem, 107 (1986) 103-163.
  • [4] R. Bott and L. W. Tu, Differentialforms in algebraic topology, Graduate Texts in Math., No. 82, Springer, Berlin, 1982.
  • [5] J. Cheeger, Eta invariants, the adiabatic approximation and conical singularities, J. Differential Geometry 26 (1987) 175-221.
  • [6] L. Hormander, The analysis of linear partial differential operators, Springer, Heidelberg, 1983.
  • [7] B. Livingston, R. R. Mazzeo and R. B. Melrose, Fibred cusps and harmonic forms, in preparation.
  • [8] R. B. Melrose, Transformation of boundary problems, Acta Math. 147 (1981) 149-236.
  • [9] R. B. Melrose, Pseudodifferential operators on manifolds with corners, to appear.
  • [10] R. B. Melrose and N. Ritter, Interactionof progressing wavesfor semilinear wave equations. II, Ark. Mat. 25 (1987) 91-114.
  • [11] E. Witten, Global gravitational anomalies, Comm. Math. Phys. 100 (1985) 197-229.