Skip to main content
Log in

Analytic torsion and closed geodesics on hyperbolic manifolds

  • Published:
Inventiones mathematicae Aims and scope

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.

References

  • [Al] Alvarez, O.: Theory of strings with boundaries: fluctuations, topology and quantum geometry. Nucl. Phys. B216, 125–184 (1983)

    Google Scholar 

  • [A] Anderson, D.R.: The Whitehead torsion of the total space of a fiber bundle. Topology11, 179–194 (1972)

    Google Scholar 

  • [AB] Atiyah, M., Bott, R.: The Lefschetz fixed point theorem for elliptic complexes, I. Ann. Math.88, 374–407 (1967)

    Google Scholar 

  • [B] Bourbaki, N.: Groupes et algebras de Lie, Chaps. IV–VI. Eléments de mathématique, Fasc. XXXIV, 1968

  • [C] Cheeger, J.: Analytic torsion and the heat equation. Ann. Math.109, 259–322 (1979)

    Google Scholar 

  • [Co] Cohen, M.: A course in simple homotopy theory. Springer GTM, 1973

  • [D] Donnelly, H. On the analytic torsion and eta invariant for negatively curved manifolds. Am. J. Math.101, 1365–1379 (1979)

    Google Scholar 

  • [Fr] Franks, J.: Knots, links and symbolic dynamics. Ann. Math.113, 529–552 (1981)

    Google Scholar 

  • [F1] Fried, D.: Homological identities for closed orbits. Invent. Math.71, 419–442 (1983)

    Google Scholar 

  • [F2] Fried, D.: Lefschetz formulas for flows. (In preparation)

  • [F3] Fried, D.: The zeta functions of Ruelle and Selberg I. (To appear in Ann. E.N.S.)

  • [F4] Fried, D.: The zeta functions of Ruelle and Selberg II. (In preparation)

  • [F5] Fried, D.: Fuchsian groups and Reidemeister torsion. (To appear in proceedings of the AMS trace formula conference, Contemporary Mathematics, 1986)

  • [F6] Fried, D.: Torsion and closed geodesics on complex hyperbolic manifolds. (Preprint)

  • [F7] Fried, D.: Eta and dynamics. (In preparation)

  • [G] Gangolli, R.: Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one. Ill. J. Math.21, 403–423 (1977)

    Google Scholar 

  • [H] Hejhal, D.: The Selberg trace formula forSL(2,R), I and II. Lect. Notes Math.548 (1976) and1001 (1983)

    Google Scholar 

  • [Mc] McKean, H.P.: Selberg's trace formula as applied to a compact Riemann surface. Commun. Pure Appl. Math.25, 225–246 (1972)

    Google Scholar 

  • [Mia] Miatello, R.J.: The Minakshisundaram-Pleijel coefficients for the vector valued heat kernel on compact locally symmetric spaces of negative curvature. Trans. Am. Math. Soc.260, 1–33 (1980)

    Google Scholar 

  • [M] Millson, J.: Closed geodesics and the η-invariant. Ann. Math.108, 1–39 (1978)

    Google Scholar 

  • [Mi] Milnor, J.: Whitehead torsion. Bull. Am. Math. Soc.72, 358–426 (1966)

    Google Scholar 

  • [Mi2] Milnor, J.: Infinite cyclic coverings. In: Conf. on the Topology of Manifolds, 115–133 (1968)

  • [Mu] Müller, W.: Analytic torsion andR-torsion of Riemannian manifolds. Adv. Math.28, 233–305 (1978)

    Google Scholar 

  • [Q] Quillen, D.: Determinants of Cauchy-Riemann operators over a Riemann surface. (Inst. Hautes Etud. Sci. preprint, July 1984)

  • [R] Randol, B.: On the analytic continuation of the Minakshisundaram-Pleijel zeta function for compact Riemann surfaces. Trans. Am. Math. Soc.201, 241–246 (1975)

    Google Scholar 

  • [RS1] Ray, D.B., I. Singer:R-Torsion and the Laplacian on Riemannian manifolds. Adv. Math.7. 145–210 (1971)

    Google Scholar 

  • [RS2] Ray, D.B., I. Singer: Analytic torsion for complex manifolds. Ann. Math.98, 154–177 (1973)

    Google Scholar 

  • [Sc] Scott, D.: Selberg type zeta functions for the group of complex two by two matrices of determinant one. Math. Ann.253, 177–194 (1980)

    Google Scholar 

  • [S] Seeley, R.: Complex powers of an elliptic operator. Proc. Symp. Pure Math.10, 288–307 (1966)

    Google Scholar 

  • [Se] Selberg, A.: Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series. J. Indian Math. Soc.20, 47–87 (1956)

    Google Scholar 

  • [Si] Singer, I.: Eigenvalues of the Laplacian and invariants of manifolds. Proceedings of the International Congress of Mathematics, Vancouver 1974

  • [W] Wallach, N.: On the Selberg trace formula in the case of compact quotient. Bull. Am. Math. Soc.82, 171–195 (1976)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Partially supported by the National Science Foundation, the Sloan Foundation and the I.H.E.S.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fried, D. Analytic torsion and closed geodesics on hyperbolic manifolds. Invent Math 84, 523–540 (1986). https://doi.org/10.1007/BF01388745

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388745

Keywords

Navigation