Geodesic spheres as generators of the homotopy groups of O,BO

DOI10.4310/jdg/1214434706zbMath0441.55013OpenAlexW1537713799WikidataQ115189333 ScholiaQ115189333MaRDI QIDQ1143040

S. H. Smith

Publication date: 1978

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/jdg/1214434706

zbMATH Keywords

Bott periodicity theoremexistence of complete Riemannian metrics of nonnegative sectional curvature on stable vectorbundles over spheresgeodesic spheres as generators of the homotopy groups of O,BO

Mathematics Subject Classification ID

Sphere bundles and vector bundles in algebraic topology (55R25) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Geodesics in global differential geometry (53C22) Global Riemannian geometry, including pinching (53C20) Homotopy groups of special spaces (55Q52)

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Metric of non-negative sectional curvature on the tangent bundle of the two-dimensional sphere ⋮ On pull-backs of the universal connection ⋮ A condition for positivity of curvature ⋮ Obstructions to nonnegative curvature and rational homotopy theory ⋮ Vector bundles of non-negative curvature over cohomogeneity one manifolds ⋮ Bounds on sectional curvature and interactions with topology ⋮ Strongly nonnegative curvature ⋮ A panoramic glimpse of manifolds with sectional curvature bounded from below ⋮ Lifting group actions and nonnegative curvature ⋮ Nonnegative curvature on stable bundles over compact rank one symmetric spaces ⋮ Suspending the Cartan embedding of \({\mathbb H}P^n\) through spindles and generators of homotopy groups ⋮ Some bundles of non-negative curvature ⋮ Open manifolds with non-homeomorphic positively curved souls ⋮ The stable converse soul question for positively curved homogeneous spaces ⋮ Finiteness theorems for nonnegatively curved vector bundles ⋮ Open manifolds of nonnegative curvature ⋮ $S\sp 3$-bundles and exotic actions

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