Rationalized evaluation subgroups of a map. I: Sullivan models, derivations and \(G\)-sequences

DOI10.1016/j.jpaa.2006.05.018zbMath1112.55012arXivmath/0309432OpenAlexW2016767722MaRDI QIDQ863905

Gregory Lupton, Samuel Bruce Smith

Publication date: 12 February 2007

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0309432

zbMATH Keywords

Gottlieb groupsderivationsminimal modelsevaluation mapevaluation subgrouprational homotopymapping spaces\(\omega\)-homology\(G\)-sequence

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Homotopy groups of special spaces (55Q52)

Related Items (26)

Relative Gottlieb groups of embeddings between complex Grassmannians ⋮ Characteristic classes for families of bundles ⋮ Evaluation subgroups of a map and the rationalized $G$-sequence ⋮ Rationalized evaluation subgroups of a map. II: Quillen models and adjoint maps ⋮ The evaluation subgroup of a fibre inclusion ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Cohomology algebra of mapping spaces between quaternion Grassmannians ⋮ Relative Gottlieb groups of mapping spaces and their rational cohomology ⋮ Generalized Rational Evaluation Subgroups of the Inclusion between Complex Projective Spaces ⋮ On the mapping space homotopy groups and the free loop space homology groups ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Gottlieb groups of homogeneous spaces ⋮ Derivations of a Sullivan model and the rationalized \(G\)-sequence ⋮ Rational homotopy of gauge groups ⋮ Realizing spaces as classifying spaces ⋮ Rationalized evaluation subgroups of mapping spaces between complex Grassmannians ⋮ Mapping spaces between manifolds and the evaluation map ⋮ On the Hochschild cohomology of a map between commutative differential graded algebras ⋮ Rank of the fundamental group of any component of a function space ⋮ Relative Gottlieb groups of the Pl\"ucker embedding of some complex Grassmanians ⋮ Hochschild cohomology of certain Koszul Sullivan Extensions

Cites Work

• Gottlieb groups of spheres
• Rationalized evaluation subgroups of a map. II: Quillen models and adjoint maps
• The rational homotopy Lie algebra of function spaces
• Rational universal fibrations and flag manifolds
• Minimal models in homotopy theory
• Infinitesimal computations in topology
• The \(G\)-sequence and the \(\omega\)-homology of a CW-pair
• Algèbre de Lie de dérivations de certaines algèbres pures
• Gottlieb groups of homogeneous spaces
• André--Quillen cohomology and rational homotopy of function spaces
• Rational evaluation subgroups
• Rank of the fundamental group of any component of a function space
• Rational Homotopy of the Space of Sections of a Nilpotent Bundle
• Obstructions to nonnegative curvature and rational homotopy theory
• Evaluation Subgroups of Homotopy Groups
• Exactness of \(G\)-sequences and monomorphisms
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