Relations in the 24-th homotopy groups of spheres
Toshiyuki Miyauchi, Juno Mukai

TL;DR
This paper proves certain non-trivial Toda brackets in the 24th homotopy groups of spheres and establishes a specific relation among elements in these groups, advancing understanding of their algebraic structure.
Contribution
It confirms a conjecture about the non-triviality of specific Toda brackets and clarifies relations among elements in the 24th homotopy groups of spheres.
Findings
Proves the non-triviality of Toda brackets <ν̄,σ,ν̄> and <ν,η,σ̄>.
Establishes the relation ν̄₇ω₁₅=ν₇σ₁₀κ₁₇ in π₃₁⁷.
Supports the conjecture on the determination of the P-image by Toda brackets.
Abstract
The main purpose of this note is to give a proof of the fact that the Toda brackets and are not trivial. This is an affirmative answer of the second author's Conjecture (Determination of the -image by Toda brackets, Geometry and Topology Monographs 13(2008), 355-383). The second purpose is to show the relation in .
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis · Geometric and Algebraic Topology
