Fried conjecture in small dimensions
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Fried conjecture in small dimensions
Auteur(s) :
Dang, Nguyen Viet [Auteur]
Probabilités, statistique, physique mathématique [PSPM]
Guillarmou, Colin [Auteur]
Université Paris-Sud - Paris 11 [UP11]
Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Shen, Shu [Auteur]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Probabilités, statistique, physique mathématique [PSPM]
Guillarmou, Colin [Auteur]
Université Paris-Sud - Paris 11 [UP11]
Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Shen, Shu [Auteur]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Titre de la revue :
Inventiones Mathematicae
Pagination :
525–579
Éditeur :
Springer Verlag
Date de publication :
2020
ISSN :
0020-9910
Discipline(s) HAL :
Mathématiques [math]
Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Géométrie différentielle [math.DG]
Résumé en anglais : [en]
We study the twisted Ruelle zeta function ζX (s) for smooth Anosov vector fields X acting on flat vector bundles over smooth compact manifolds. In dimension 3, we prove Fried conjecture, relating Reidemeister torsion and ...
Lire la suite >We study the twisted Ruelle zeta function ζX (s) for smooth Anosov vector fields X acting on flat vector bundles over smooth compact manifolds. In dimension 3, we prove Fried conjecture, relating Reidemeister torsion and ζX (0). In higher dimensions, we show more generally that ζX (0) is locally constant with respect to the vector field X under a spectral condition. As a consequence, we also show Fried conjecture for Anosov flows near the geodesic flow on the unit tangent bundle of hyperbolic 3-manifolds. This gives the first examples of non-analytic Anosov flows and geodesic flows in variable negative curvature where Fried conjecture holds true.Lire moins >
Lire la suite >We study the twisted Ruelle zeta function ζX (s) for smooth Anosov vector fields X acting on flat vector bundles over smooth compact manifolds. In dimension 3, we prove Fried conjecture, relating Reidemeister torsion and ζX (0). In higher dimensions, we show more generally that ζX (0) is locally constant with respect to the vector field X under a spectral condition. As a consequence, we also show Fried conjecture for Anosov flows near the geodesic flow on the unit tangent bundle of hyperbolic 3-manifolds. This gives the first examples of non-analytic Anosov flows and geodesic flows in variable negative curvature where Fried conjecture holds true.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
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