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2 results

  • Marked length pattern rigidity for arithmetic manifolds

  • Part of
  • YANLONG HAO
  • Journal:
    Ergodic Theory and Dynamical Systems , First View
    Published online by Cambridge University Press:
    30 September 2024, pp. 1-25
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  • In this paper, we prove a cocycle version of marked length spectrum rigidity. There are two consequences: the first one is marked length pattern rigidity for arithmetic hyperbolic locally symmetric manifolds, and the second one is a strengthened marked length spectrum rigidity for surfaces and closed locally symmetric manifolds.

  • AUTOMORPHIC LEFSCHETZ PROPERTIES FOR NONCOMPACT ARITHMETIC MANIFOLDS

  • Part of
  • Arvind N. Nair, Ankit Rai
  • Journal:
    Journal of the Institute of Mathematics of Jussieu / Volume 22 / Issue 4 / July 2023
    Published online by Cambridge University Press:
    18 October 2021, pp. 1655-1702
    Print publication:
    July 2023
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  • We prove the injectivity of Oda-type restriction maps for the cohomology of noncompact congruence quotients of symmetric spaces. This includes results for restriction between (1) congruence real hyperbolic manifolds, (2) congruence complex hyperbolic manifolds, and (3) orthogonal Shimura varieties. These results generalize results for compact congruence quotients by Bergeron and Clozel [Quelques conséquences des travaux d’Arthur pour le spectre et la topologie des variétés hyperboliques, Invent. Math. 192 (2013), 505–532] and Venkataramana [Cohomology of compact locally symmetric spaces, Compos. Math. 125 (2001), 221–253]. The proofs combine techniques of mixed Hodge theory and methods involving automorphic forms.