# Topology of Pollicott-Ruelle resonant states

@article{Dang2017TopologyOP, title={Topology of Pollicott-Ruelle resonant states}, author={Nguyen Viet Dang and Gabriel Rivi{\`e}re}, journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE}, year={2017} }

We prove that the twisted De Rham cohomology of a flat vector bundleover some smooth manifold is isomorphic to the cohomology of invariant Pollicott--Ruelleresonant states associated with Anosov and Morse--Smale flows. As a consequence, weobtain generalized Morse inequalities for such flows. In the case of Morse--Smale flows,we relate the resonances lying on the imaginary axis with the twisted Fuller measuresused by Fried in his work on Reidemeister torsion. In particular, when V is a…

## 13 Citations

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We study the twisted Ruelle zeta function $$\zeta _X(s)$$ ζ X ( s ) for smooth Anosov vector fields X acting on flat vector bundles over smooth compact manifolds. In dimension 3, we prove the Fried…

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