Eichler-Shimura Homology, Intersection Numbers and Rational Structures on Spaces of Modular Forms

DOI10.2307/2000367zbMath0618.10020OpenAlexW4242147614MaRDI QIDQ3754674

John J. Millson, Svetlana Katok

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000367

zbMATH Keywords

cohomology classclosed geodesiclocal coefficientsKronecker indexperiod of cusp formdecomposable cyclesEichler-Shimura periods

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Structure of modular groups and generalizations; arithmetic groups (11F06) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Homology with local coefficients, equivariant cohomology (55N25)

Related Items

Closed geodesics and pluricanonical sections on ball quotients ⋮ Eichler-Shimura homology and the finite generation of cusp forms by hyperbolic Poincaré series ⋮ Small spanning sets of cusp forms ⋮ On vector-valued automorphic forms on bounded symmetric domains ⋮ Modulformen auf \(\Gamma_ 0(N)\) mit rationalen Perioden. (Modular forms for \(\Gamma_ 0(N)\) with rational periods) ⋮ Holomorphic Automorphic Forms and Cohomology ⋮ Automorphic forms, definite quaternion algebras, and Atkin-Lehner theory on trees ⋮ Closed geodesics and periods of automorphic forms ⋮ Mixed cusp forms and Poincaré series ⋮ Geodesics in homology classes and periods of automorphic forms ⋮ On the Kronecker pairing for mixed cusp forms

Cites Work

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• Harmonic differentials and closed geodesics on a Riemann surface
• On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds
• Deformation spaces associated to compact hyperbolic manifolds