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Anosov foliations and cohomology

Published online by Cambridge University Press:  19 September 2008

David Fried
David Fried
Affiliation:
Department of Mathematics, Boston University, Boston, MA 02215, USA
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Abstract

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The cohomology action of an Anosov diffeomorphism on a nilmanifold resembles that of a Cartesian product map. Corresponding results hold for infranilmanifolds, giving an invariant bigrading of the cohomology and a fourfold symmetry that extends Poincaré duality. Holonomy invariant cocycles are applied to the action on first cohomology.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 1 , March 1986 , pp. 9 - 16
Copyright
Copyright © Cambridge University Press 1986

References

REFERENCES

[1]Bowen, R.. On Axiom A diffeomorphisms. CBMS Reg. conf. 35, Providence, 1978.Google Scholar
[2]Farrell, T. & Jones, L.. Markov cell structures. Bull. Amer. Math. Soc. 83 (1977), 739–740.CrossRefGoogle Scholar
[3]Franks, J.. Anosov diffeomorphisms. In Proc. Symp. Pure Math. XIV. Global Analysis. Providence, 1970, 61–94.Google Scholar
[4]Fried, D.. Flow equivalence, hyperbolic systems and a new zeta function for flows. Comm. Math. Helv. 57 (1982), 237–259.CrossRefGoogle Scholar
[5]Hirsch, M.. Anosov maps, polycyclic groups and homology. Topology 10 (1971), 177–183.CrossRefGoogle Scholar
[6]Manning, A.. There are no new Anosov diffeomorphisms on tori. Amer. J. Math. 96 (1974), 422–429.CrossRefGoogle Scholar
[7]Nomizu, K.. On the cohomology of compact homogeneous spaces of nilpotent Lie groups. Annals Math. 59 (1954), 531–538.CrossRefGoogle Scholar
[8]Ruelle, D. & Sullivan, D.. Currents, flows and diffeomorphisms. Topology 14 (1975), 319–328.CrossRefGoogle Scholar
[9]Shub, M.. Alexander cocycles and dynamics. Asterisque 51 (1978), 395–414.Google Scholar
[10]Shub, M. & Williams, R.. Entropy and Stability. Topology 14 (1975), 329–338.CrossRefGoogle Scholar