Dénombrement des types de K-homotopie. Théorie de la déformation

DOI10.24033/msmf.288zbMath0452.55005OpenAlexW1957120067MaRDI QIDQ3899187

Yves Félix

Publication date: 1980

Published in: Mémoires de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=MSMF_1980_2_3__1_0

zbMATH Keywords

rigiditydeformationdifferential graded commutative algebraalgebraic variety on which an algebraic group actscohomology algebras which have a unique rational homotopy typedeforming the differentialK-homotopyKoszul-Sullivan minimal model of differential filtered graded algebraobstructions to rigidityobstructions to uniqueness of homotopy typerational homotopy types that have a given cohomology algebraupper semi-continuity of homotopy invariants

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Group actions on varieties or schemes (quotients) (14L30) Topological transformation groups (57S99) Minimal model program (Mori theory, extremal rays) (14E30) Automorphic forms, one variable (11F12) Homotopy theory and fundamental groups in algebraic geometry (14F35) Deformations and infinitesimal methods in commutative ring theory (13D10) Modules of differentials (13N05)

Related Items (12)

A cohomology theory for \(A(m)\)-algebras and applications ⋮ Moduli spaces for generic low-dimensional complexes ⋮ Rétractes d'un espace. (Retracts of a space.) ⋮ The deformation complex for differential graded Hopf algebras ⋮ Eilenberg-Moore Models for Fibrations ⋮ C-symplectic poset structure on a simply connected space ⋮ The homotopy automorphisms of a marked n-stage ⋮ \(p\)-formality of spaces ⋮ Fiber-homotopy self-equivalences and a classification of fibrations in rational homotopy ⋮ Homotopy Lie algebras and fundamental groups via deformation theory ⋮ Loop space homology -- problems and questions ⋮ Geometric decompositions, algebraic models and rigidity theorems

Cites Work

• Homotopy types within a rational homotopy type
• Infinitesimal computations in topology
• Obstructions to homotopy equivalences
• Algebraic geography: Varieties of structure constants
• Rational homotopy theory
• Matric Massey products
• On the deformation of rings and algebras
• On 𝑃𝐿 de Rham theory and rational homotopy type
• Cohomology and deformations in graded Lie algebras
• Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes
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