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The convergence of the product γ˜p-1h0bn-1 in the Adams spectral sequence

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Published/Copyright: April 27, 2013
Forum Mathematicum
From the journal Forum Mathematicum Volume 27 Issue 3

Abstract

Let p be a prime with p ≥ 7 and q=2(p-1). In this paper we prove the existence of a nontrivial product of filtration p + 2 in the stable homotopy groups of spheres π(pn+p3-p-2)q-6S. This nontrivial product is shown to be represented up to a nonzero scalar by the product element

γ˜p-1h0bn-1∈ Ext 𝒜p+2,(pn+p3-p-2)q+p-4(ℤ/p,ℤ/p)

in the Adams spectral sequence where n ≥ 1 and n ≥ 4.

Keywords: Stable homotopy groups of spheres; Adams spectral sequence; May spectral sequence
MSC: 55Q45

Funding source: NSFC

Award Identifier / Grant number: 11101161

Funding source: NSFC

Award Identifier / Grant number: 11261062

Funding source: Research Fund for the Doctoral Program of Higher Education of China

Award Identifier / Grant number: 20114407120011

The authors would like to thank the referee for his/her many helpful suggestions.

Received: 2012-11-8
Revised: 2013-3-4
Published Online: 2013-4-27
Published in Print: 2015-5-1

© 2015 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Nielsen numbers of maps of aspherical figure-eight type polyhedra
  3. Simplicial geometry of unital lattice-ordered abelian groups
  4. Upper triangular matrices and operations in odd primary connective K-theory
  5. Solving quintic equations by two-fold origami
  6. Orthogonality of polynomials and orthosymmetry
  7. The moduli space of 4-dimensional non-nilpotent complex associative algebras
  8. Improvement of eigenfunction estimates on manifolds of nonpositive curvature
  9. Unramified representations of the universal central extension of SL2(𝔽q((z)))
  10. Languages associated with saturated formations of groups
  11. On some new model category structures from old, on the same underlying category
  12. On functions of bounded Λ-variation and integral smoothness
  13. Ring coproducts embedded in power-series rings
  14. A uniform bound for geodesic periods of eigenfunctions on hyperbolic surfaces
  15. Action-induced nested classes of groups and jump (co)homology
  16. The convergence of the product γ˜p-1h0bn-1 in the Adams spectral sequence
  17. Product graphs, sum-product graphs and sum-product estimates over finite rings
  18. BV functions in a Gelfand triple for differentiable measure and its applications
  19. The variety of nilpotent elements and invariant polynomial functions on the special algebra Sn
  20. The Lefschetz coincidence class of p maps
  21. The natural pseudo-distance as a quotient pseudo-metric, and applications
  22. On a class of parametric Neumann problems with indefinite and unbounded potential
  23. An estimate on the heat kernel of Schrödinger operators with non-negative potentials on nilpotent Lie groups and its applications
  24. A hybrid Euler–Hadamard product and moments of ζ'(ρ)
  25. Legendrian realization in convex Lefschetz fibrations and convex stabilizations
  26. Recollements induced from tilting modules over tame hereditary algebras
  27. Corrigendum to On some multiplicity and mixed multiplicity formulas [Forum Math. 26 (2014), 413–442]
https://doi.org/10.1515/forum-2012-0162
Keywords for this article
Stable homotopy groups of spheres; Adams spectral sequence; May spectral sequence

Articles in the same Issue

  1. Frontmatter
  2. Nielsen numbers of maps of aspherical figure-eight type polyhedra
  3. Simplicial geometry of unital lattice-ordered abelian groups
  4. Upper triangular matrices and operations in odd primary connective K-theory
  5. Solving quintic equations by two-fold origami
  6. Orthogonality of polynomials and orthosymmetry
  7. The moduli space of 4-dimensional non-nilpotent complex associative algebras
  8. Improvement of eigenfunction estimates on manifolds of nonpositive curvature
  9. Unramified representations of the universal central extension of SL2(𝔽q((z)))
  10. Languages associated with saturated formations of groups
  11. On some new model category structures from old, on the same underlying category
  12. On functions of bounded Λ-variation and integral smoothness
  13. Ring coproducts embedded in power-series rings
  14. A uniform bound for geodesic periods of eigenfunctions on hyperbolic surfaces
  15. Action-induced nested classes of groups and jump (co)homology
  16. The convergence of the product γ˜p-1h0bn-1 in the Adams spectral sequence
  17. Product graphs, sum-product graphs and sum-product estimates over finite rings
  18. BV functions in a Gelfand triple for differentiable measure and its applications
  19. The variety of nilpotent elements and invariant polynomial functions on the special algebra Sn
  20. The Lefschetz coincidence class of p maps
  21. The natural pseudo-distance as a quotient pseudo-metric, and applications
  22. On a class of parametric Neumann problems with indefinite and unbounded potential
  23. An estimate on the heat kernel of Schrödinger operators with non-negative potentials on nilpotent Lie groups and its applications
  24. A hybrid Euler–Hadamard product and moments of ζ'(ρ)
  25. Legendrian realization in convex Lefschetz fibrations and convex stabilizations
  26. Recollements induced from tilting modules over tame hereditary algebras
  27. Corrigendum to On some multiplicity and mixed multiplicity formulas [Forum Math. 26 (2014), 413–442]
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