Skip to main content
Log in

A local analytic splitting of the holonomy map on flat connections

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Atiyah, M., Patodi, V., Singer, I.: Spectral asymmetry and Riemannian geometry. I. Math. Proc. Camb. Philos. Soc.77, 43–69 (1975)

    Google Scholar 

  2. Atiyah, M., Patodi, V., Singer, I.: Spectral asymmetry and Riemannian geometry. II. Math. Proc. Camb. Philos. Soc.78, 405–432 (1975)

    Google Scholar 

  3. Atiyah, M., patodi, V., Singer, I.: Spectral asymmetry and Riemannian geometry. III. Math. Proc. Camb. Philos. Soc.79, 71–99 (1976)

    Google Scholar 

  4. Berline N., Getzler, E., Vergne, M.: Heat kernels and Dirac operators. (Grundlehren Math. Wiss., 298) 1991 Berlin Heidelberg New York: Springer

    Google Scholar 

  5. Cappell, S., Lee, R., Miller, E.: (Preprint)

  6. Gilkey, P.: Invariance theory, the heat equation, and the Atiyah-Singer index theorem. (Math. Lect. Ser. vol. 11) Wilmington: Publish or Perish 1984

    Google Scholar 

  7. Gunning, R.: Introduction to holomorphic functions of several variables, vol. I. Belmont: Wadsworth & Brooks/Cole 1990

    Google Scholar 

  8. Goldman, W., Millson, J.: The deformation theory of representations of fundamental groups of compact Kahler manifolds. Publ. Math., Inst. Hautes Étud. Sci.67, 43–96 (1988)

    Google Scholar 

  9. Goldman, W., Millson, J.: The homotopy invariance of the Kuranishi space. III. J. Math.34 (no. 2) 337–367 (1990)

    Google Scholar 

  10. Hille, E.: Functional analysis and semi-groups. (Colloq. Publ., Am. Math. Soc., vol. XXXI) Providence, RI: Am. Math. Soc. 1948

    Google Scholar 

  11. Kato, T.: Perturbation theory for linear operators, second edition. (Grundlehren Math. Wiss., 132) 1976 Berlin Heidelberg New York: Springer

    Google Scholar 

  12. Kirk, P., Klassen, E.: Computing spectral flow via cup products. (to appear in J. Differ. Geom.)

  13. Kirk, P., Klassen, E.: The spectral flow of the odd signature operator on a manifold with boundary (preprint 1993)

  14. Lefschetz, S.: Differential equations: Geometric theory, second edition. New York: Interscience

  15. Levine, J.: Link invariants via eta invariants. (Preprint 1992)

  16. Ramadas, T.R., Singer, I., Weitsman, J.: Some comments on Chern-Simons Gauge theory. Commun. Math. Phys.126, 409–420 (1989)

    Google Scholar 

  17. Yoshida, T.: Floer homology and splittings of manifolds. Ann. Math.134, 277–324 (1991)

    Google Scholar 

  18. Zorn, M.: Derivatives and Fréchet differentials. Bull. Am. Math. Soc.52, 133–137 (1946)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported by the National Science Foundation

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fine, B., Kirk, P. & Klassen, E. A local analytic splitting of the holonomy map on flat connections. Math. Ann. 299, 171–189 (1994). https://doi.org/10.1007/BF01459778

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01459778

Mathematics Subject Classification (1991)

Navigation