Geodesics in homology classes

DOI10.1215/S0012-7094-87-05515-3zbMath0642.53050MaRDI QIDQ1101700

Peter C. Sarnak, Ralph S. Phillips

Publication date: 1987

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

hyperbolic manifoldasymptotic behaviourfundamental groupclosed geodesics

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Geodesics in global differential geometry (53C22) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (41)

Number variance for arithmetic hyperbolic surfaces ⋮ Splitting of Geodesics in Homology Classes ⋮ A local limit theorem for closed geodesics and homology ⋮ Asymptotics for closed geodesics in a homology class, the finite volume case ⋮ An explicit prime geodesic theorem for discrete tori and the hypergeometric functions ⋮ A trace formula for non-unitary representations of a uniform lattice ⋮ Chebyshev's Bias ⋮ Linking numbers of modular geodesics ⋮ Dynamical 𝐿-functions and homology of closed orbits ⋮ On the local-global conjecture for commutator traces ⋮ Concentration of closed geodesics in the homology of modular curves ⋮ Large degree covers and sharp resonances of hyperbolic surfaces ⋮ Closed geodesics with prescribed intersection numbers ⋮ Prime orbit theorems for expanding Thurston maps: Dirichlet series and orbifolds ⋮ Counting geodesics of given commutator length ⋮ Mini-workshop: (Anosov)\(^3\). Abstracts from the mini-workshop held December 5--11, 2021 (hybrid meeting) ⋮ Spectral deformations of automorphic functions over graphs of groups ⋮ Equidistribution of geodesics on homology classes and analogues for free groups ⋮ Anosov flows, growth rates on covers and group extensions of subshifts ⋮ Equidistribution of holonomy about closed geodesics ⋮ The spectrum of Fermat curves ⋮ Sub-leading asymptotics of ECH capacities ⋮ Linking numbers of modular knots ⋮ Chebotarev-type theorems in homology classes ⋮ Closed geodesics and periods of automorphic forms ⋮ New directions in Nielsen-Reidemeister theory ⋮ Pairs of periodic orbits with fixed homology difference ⋮ Zeta functions, 3-manifolds and asymptotics in Nielsen theory ⋮ Growth in free groups (and other stories) -- twelve years later ⋮ THE PRIME GEODESIC THEOREM AND QUANTUM MECHANICS ON FINITE VOLUME GRAPHS: A REVIEW ⋮ On Selberg's small eigenvalue conjecture and residual eigenvalues ⋮ Precise counting results for closed orbits of Anosov flows ⋮ Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux ⋮ Trace formula for compact \(\Gamma \setminus PSL_ 2({\mathbb{R}})\) and the equidistribution theory of closed geodesics ⋮ Analytic torsion for line bundles on Riemann surfaces ⋮ Positive harmonic functions on abelian covers ⋮ Smooth mixing Anosov flows in dimension three are exponentially mixing ⋮ Closed orbits in homology classes ⋮ Closed orbits in homology classes for Anosov flows ⋮ Closed geodesics in homology classes on surfaces of variable negative curvature ⋮ Geodesics in homology classes and periods of automorphic forms

Cites Work

• Homology of closed geodesics in a negatively curved manifold
• Applications of ergodic theory to the investigation of manifolds of negative curvature
• The spectral theory of geometrically periodic hyperbolic 3-manifolds
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