Mixed Hodge structures on homotopy groups

DOI10.1090/S0273-0979-1986-15410-8zbMath0597.55009OpenAlexW1967347027MaRDI QIDQ3730651

Richard M. Hain

Publication date: 1986

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1986-15410-8

zbMATH Keywords

varietiesbar constructionhomotopy groupssmooth varietyasymptotic Hodge theoryhomotopy fibers of morphisms between varietiesperiods of iterated integrals

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Loop spaces (55P35) Bar and cobar constructions (57T30) Homotopy theory and fundamental groups in algebraic geometry (14F35) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Operations in homotopy groups (55Q35)

Related Items

The de Rham homotopy theory of complex algebraic varieties. I, Position of singularities of hypersurfaces and the topology of their complements, Mixed Hodge structure in cyclic homology and algebraic K-theory. I, Rational homotopy of complex projective varieties with normal isolated singularities, Mixed Hodge structures on the homotopy of links

Cites Work

• Harmonic volumes
• Unipotent variations of mixed Hodge structure
• The de Rham homotopy theory of complex algebraic varieties. I
• Limits of Hodge structures
• Real homotopy theory of Kähler manifolds
• The algebraic topology of smooth algebraic varieties
• Mixed Hodge structures on the homotopy of links
• Lectures on minimal models
• Iterated integrals and homotopy periods
• Finiteness in the Minimal Models of Sullivan
• Iterated path integrals