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Lefschetz formulae for Anosov flows on 3-manifolds

Published online by Cambridge University Press:  19 September 2008

Héctor Sánchez-Morgado
Héctor Sánchez-Morgado
Affiliation:
Institute de Matematicas, Universidad Nacional Autónoma de México, Ciudad Universitaria CP 04510, Mexico D.F., Mexico
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Abstract

Fried has related closed orbits of the geodesic flow of a surface S of constant negative curvature to the R-torsion for a unitary representation of the fundamental group of the unit tangent bundle T1S. In this paper we extend those results to transitive Anosov flows and 2-dimensional attractors on 3-manifolds.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 2 , June 1993 , pp. 335 - 347
Copyright
Copyright © Cambridge University Press 1993

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References

REFERENCES

[1]Bott, R. & Tu, L. W.. Differential Forms in Algebraic Topology, GTM 82. Springer, New York, 1981.Google Scholar
[2]Christy, J.. Branched surfaces and attractors I: dynamic branched surfaces.Google Scholar
[3]Fried, D.. Fuchsian groups and Reidemeister torsion. Contemp. Math. S3 (1986), 141–163.CrossRefGoogle Scholar
[4]Fried, D.. The zeta functions of Ruelle and Selberg I. Ann. Sci. ENS 19 (1986), 491–517.Google Scholar
[5]Fried, D.. Lefschetz formulae for flows. Contemp. Math. 58 (1987), 19–69.CrossRefGoogle Scholar
[6]Ratner, M.. Markov decomposition for a Y-flow on a three-dimensional manifold. Math. Notes 6 (1969), 880–886.CrossRefGoogle Scholar
[7]Ruelle, D.. Zeta functions for expanding maps and Anosov flows. Invent. Math. 34 (1976), 231–242.CrossRefGoogle Scholar