Periods of abelian differentials and dynamics

DOI10.1090/conm/744/14989zbMath1436.37047arXiv1710.11234OpenAlexW3016566369MaRDI QIDQ3296003

Michael Kapovich

Publication date: 3 July 2020

Published in: Dynamics: Topology and Numbers (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.11234

zbMATH Keywords

abelian differentials

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) Period matrices, variation of Hodge structure; degenerations (32G20) Discrete subgroups of Lie groups (22E40) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Related Items (7)

Real-normalized differentials with a single order 2 pole ⋮ Mapping class group dynamics on \(\operatorname{Aff}(\mathbb{C})\)-characters ⋮ Holonomy of complex projective structures on surfaces with prescribed branch data ⋮ Translation surfaces and periods of meromorphic differentials ⋮ A transfer principle: from periods to isoperiodic foliations ⋮ Haupt's theorem for strata of abelian differentials ⋮ Deformation quantization of moduli spaces of Higgs bundles on a Riemann surface with translation structure

Cites Work

• Orbits of horospherical flows
• On Raghunathan's measure conjecture
• Monodromy groups and linearly polymorphic functions
• Lie groups and Lie algebras III. Structure of Lie groups and Lie algebras. Transl. from the Russian by V. Minachin
• The monodromy groups of Schwarzian equations on closed Riemann surfaces
• On monodromy of complex projective structures
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