Codimension one immersions and the Kervaire invariant one problem

DOI10.1017/S0305004100058941zbMath0479.57016MaRDI QIDQ3938234

Peter J. Eccles

Publication date: 1981

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

zbMATH Keywords

Thom-Pontrjagin-construction(n+1)-adic constructionbordism group of immersions of n-manifolds into (n+1)-spaceelement of Hopf-invariant oneframed (n+1)-manifold with Kervaireinvariant oneKahn-Priddy-mapnumber of (n+1)-fold points of selftransverse immersionsstable Hopf-invariant

Mathematics Subject Classification ID

Differentiable structures in differential topology (57R55) Immersions in differential topology (57R42) Hopf invariants (55Q25)

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Pontryagin--Thom construction for approximation of mappings by embeddings ⋮ Double point self-transverse immersions of \(M^{8k}\looparrowright \mathbb R^{16k-4}\) ⋮ Geometric approach to stable homotopy groups of spheres. The Adams-Hopf invariants ⋮ Geometric approach to stable homotopy groups of spheres. Kervaire invariants. II. ⋮ Unnamed Item ⋮ On non-immersibility of \(\mathbb RP^{10}\) to \(\mathbb R^{15}\) ⋮ Double point of self-transverse immersions of \(M^{2n} \looparrowright R^{4n-5}\) ⋮ A categorical context for the james-hopf maps ⋮ Double point self-intersection surfaces of immersions ⋮ Cubulations, immersions, mappability and a problem of habegger ⋮ Cospherical classes in some iterated loop spaces on spheres ⋮ Freudenthal's theorem and spherical classes in H_*QS⁰ ⋮ Spherical classes in \(H_*(\omega ^ls^{l+n};{\mathbb{Z}}/2)\) for \(4\leqslant l \leqslant 8\)

Cites Work

• On the suspension triad
• On the non-existence of elements of Hopf invariant one
• \(\Gamma^+\)-structures. III: The stable structure of \(\Omega^\infty\Sigma^\infty A\)
• The homology of iterated loop spaces
• Self-intersections and higher Hopf invariants
• Multiple points of immersions and the Kahn-Priddy theorem
• On the structure of Hopf algebras
• Some differentials in the Adams spectral sequence
• On Hopf invariants
• The Kervaire invariant of framed manifolds and its generalization
• The nilpotency of elements of the stable homotopy groups of spheres
• Quelques propriétés globales des variétés différentiables
• Secondary Cohomology Operations: Two Formulas
• Immersions of Manifolds
• Triple Points and Surgery of Immersed Surfaces
• A Stable Decomposition of ω ^N Sⁿ X
• Homology of Iterated Loop Spaces
• Cobordism groups of immersions

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