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Spectral sequences and adiabatic limits

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A Taylor series analysis of the Laplacian as the underlying manifold is demormed leads to a Hodge theoretic derivation of the Leray spectral sequence.

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References

  • [Bi-Fr] Bismut, J.-M., Freed, D. S.: The analysis of Elliptic Families, I. Metrics and Connections on Determinant Bundles. Commun. Math. Phys.106, 159–176 (1986); II. Dirac Operators Eta Invariants and the Holonomy Theorem.107, 103–163 (1986)

    Google Scholar 

  • [Bi-Ch] Bismut, J.-M., Cheeger, J.: η-Invariants and Their Adiabatic Limits. J. Am. Math. Soc.2, 33–70 (1989)

    Google Scholar 

  • [Bo-Tu] Bott, R. Tu, L. W.: Differential Forms in Algebraic Topology. Graduate Texts in Mathematics no.82, Berlin Heidelberg, New York: Springer, 1982

    Google Scholar 

  • [Ch] Cheeger, J.: Eta Invariants, the Adiabatic Approximation and Conical Singularities. J. Diff. Geom.26, 175–221 (1987)

    Google Scholar 

  • [Dai] Dai, X.: Adiabatic Limits, Non-multiplicity of Signature and the Leray Spectral Sequence., J. Am. Math. Soc.4, 265–321 (1991)

    Google Scholar 

  • [Du-Sc] Dunford, N., Schwartz, J.: Linear Operators Part II. Pure and Applied Mathematics, Vol.VII New York: Interscience Publishers, 1963

    Google Scholar 

  • [Fo] Forman, R.: Hodge Theory and Spectral Sequences. Topology33, 591–611 (1994)

    Google Scholar 

  • [Ma-Me] Mazzeo, R. R., Melrose, R. B.: The Adiabatic Limit, Hodge Cohomology and Leray's Spectral Sequence for a Fibration. J. Diff. Geom.31, 185–213 (1990)

    Google Scholar 

  • [McC] McClearly, J.: User's Guide to spectral Sequences. Mathematics Lecture Series no.12, Berkeley: Publish or Perish, Inc., 1985

    Google Scholar 

  • [Mo] Molino, P.: Riemannian Foliations, Progress in Mathematics no.73, Baset, Boston: Birkhäuser, 1988

    Google Scholar 

  • [Re] Reinhart, B. L.: Differential Geometry of Foliations. Ergebnisse der mathematik und ihrer Grenzgebiete no.99, Berlin, Heidelberg, New York: Springer, 1983

    Google Scholar 

  • [Sa] Sarkaria, K. S.: A Finiteness Theorem for Foliated Manifolds. J. Math. Soc. Japan30, 687–96 (1978)

    Google Scholar 

  • [Wi] Witten, E.: Global Gravitational Anomalies. Commun. Math. Phys,100, 197–229 (1985)

    Google Scholar 

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Communicated by A. Connes

Partially supported by an NSF postdoctoral fellowship

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Forman, R. Spectral sequences and adiabatic limits. Commun.Math. Phys. 168, 57–116 (1995). https://doi.org/10.1007/BF02099584

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  • DOI: https://doi.org/10.1007/BF02099584

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