The fundamental group of a Riemann surface: Mixed Hodge structures and algebraic cycles

DOI10.1215/S0012-7094-88-05732-8zbMath0678.14005OpenAlexW1505923038MaRDI QIDQ1123938

Michael J. Pulte

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1215/s0012-7094-88-05732-8

zbMATH Keywords

Riemann surfacesfundamental groupsmixed Hodge structureTorelli type theorem

Mathematics Subject Classification ID

Jacobians, Prym varieties (14H40) Coverings of curves, fundamental group (14H30) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Transcendental methods of algebraic geometry (complex-analytic aspects) (32J25) Riemann surfaces (30F99)

Related Items

The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles, The fundamental group and extensions of motives of Jacobians of curves, The mixed Hodge structure on the fundamental group of a punctured Riemann surface, A non-abelian analogue of Whitney's 2-isomorphism theorem, Unnamed Item, On the Abel-Jacobi maps of Fermat Jacobians, A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic, Normal functions and the height of Gross-Schoen cycles, The extension of Johnson's homomorphism from the Torelli group to the mapping class group, Combinatorial iterated integrals and the harmonic volume of graphs, Harmonic Volume, Symmetric Products, and the Abel-Jacobi Map, Pointed harmonic volume and its relation to the extended Johnson homomorphism, Algebraic cycles and the mixed Hodge structure on the fundamental group of a punctured curve, On the harmonic volume of Fermat curves, The harmonic volumes of hyperelliptic curves, Quadratic Periods of Meromorphic Forms on Punctured Riemann Surfaces

Cites Work

• Harmonic volumes
• The algebraic topology of smooth algebraic varieties
• On compactifications of the quotient spaces for arithmetically defined discontinuous groups
• A new proof of Torelli's theorem
• Periods of integrals on algebraic manifolds. III: Some global differential-geometric properties of the period mapping
• Théorie de Hodge. II. (Hodge theory. II)
• Homological versus algebraic equivalence in a jacobian
• Iterated path integrals
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