On conjectures of Moore and Serre in the case of torsion-free suspensions

DOI10.1017/S0305004100060916zbMath0522.55010WikidataQ122900093 ScholiaQ122900093MaRDI QIDQ3672716

P. S. Selick

Publication date: 1983

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

rational homotopySerre conjecturehomotopy exponentMoore conjectureJames constructione-invariantfinite simply connected CW-complexp- torsion in homotopy groupstorsion-free suspensions

Mathematics Subject Classification ID

Stable classes of vector space bundles in algebraic topology and relations to (K)-theory (55R50) Rational homotopy theory (55P62) Homotopy groups, general; sets of homotopy classes (55Q05) Localization and completion in homotopy theory (55P60) Topological (K)-theory (55N15) Hopf invariants (55Q25) (K)-theory operations and generalized cohomology operations in algebraic topology (55S25)

Related Items (4)

\(p\)-hyperbolicity of homotopy groups via \(K\)-theory ⋮ Exponential growth of homotopy groups of suspended finite complexes ⋮ Modular representations and the homotopy of low rank \(p\)-local \(CW\)-complexes ⋮ Moore's conjecture for polyhedral products

Cites Work

• On the suspension triad
• The suspension triad of a sphere
• Vector bundles and the Künneth formula
• The double suspension and exponents of the homotopy groups of spheres
• Odd primary torsion in \(\pi_k(S^3)\)
• Torsion in homotopy groups
• The image of J in the EHP sequence
• On the groups \(J(X)\). IV
• On the sphere of origin of infinite families in the homotopy groups of spheres
• The splitting of the Künneth sequence for generalized cohomology
• Cohomologie modulo 2 des complexes d'Eilenberg-MacLane
• Reduced product spaces
• A remark on a theorem of J. P. Serre
• 3-primary exponents
• Vector fields on spheres

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