Obstructions to nonnegative curvature and rational homotopy theory

DOI10.1090/S0894-0347-02-00418-6zbMath1027.53036arXivmath/0007007MaRDI QIDQ4794621

Vitali Kapovitch, Igor Belegradek

Publication date: 19 February 2003

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

Full work available at URL: https://arxiv.org/abs/math/0007007

zbMATH Keywords

derivationnonnegative curvaturesoulHalperin's conjecture

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (19)

Conditions for nonnegative curvature on vector bundles and sphere bundles. ⋮ A note on the Petersen-Wilhelm conjecture ⋮ Vector bundles of non-negative curvature over cohomogeneity one manifolds ⋮ Rationalized evaluation subgroups of a map. I: Sullivan models, derivations and \(G\)-sequences ⋮ Non-formal homogeneous spaces ⋮ Bounds on sectional curvature and interactions with topology ⋮ Positive weights and self-maps ⋮ Sullivan minimal models of classifying spaces for non-formal spaces of small rank ⋮ Higher Nash blow-up local algebras of singularities and its derivation Lie algebras ⋮ A panoramic glimpse of manifolds with sectional curvature bounded from below ⋮ Rational homotopy theory and nonnegative curvature ⋮ Lifting group actions and nonnegative curvature ⋮ Positive curvature and rational ellipticity ⋮ Nonnegative curvature on stable bundles over compact rank one symmetric spaces ⋮ Non-aspherical ends and non-positive curvature ⋮ An Example of a Fiber in Fibrations Whose Serre Spectral Sequences Collapse ⋮ On the topology of positively curved Bazaikin spaces ⋮ Non-existence of negative weight derivations on positively graded Artinian algebras ⋮ The stable converse soul question for positively curved homogeneous spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Plongements différentiables de variétés dans variétés
• Some topological properties of Kaehler manifolds and homogeneous spaces
• Rational fibrations, homogeneous spaces with positive Euler characteristics and Jacobians
• Geodesic spheres as generators of the homotopy groups of O,BO
• New examples of manifolds with strictly positive curvature
• Cohomology of biquotients
• Infinitesimal computations in topology
• Algèbre de Lie de dérivations de certaines algèbres pures
• On the topology of double coset manifolds
• On a certain family of closed 13-dimensional Riemannian manifolds of positive curvature
• Curvature and symmetry of Milnor spheres
• On fundamental groups of manifolds of nonnegative curvature
• Manifolds with positive sectional curvature almost everywhere.
• Inhomogeneous spaces of positive curvature
• Contributions of rational homotopy theory to global problems in geometry
• Some examples of manifolds of nonnegative curvature
• Finiteness theorems for nonnegatively curved vector bundles
• On complete metrics of nonnegative curvature on 2-plane bundles
• Simply connected manifolds of positive scalar curvature
• On the structure of complete manifolds of nonnegative curvature
• Compact homogeneous Riemannian manifolds with strictly positive curvature
• On the Free Loop Space of Homogeneous Spaces
• Finiteness in the Minimal Models of Sullivan
• Vector Bundles with No Soul
• The metric projection onto the soul
• Symplectic manifolds with no Kähler structure
• Topological obstructions to nonnegative curvature

This page was built for publication: Obstructions to nonnegative curvature and rational homotopy theory