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- W2611750399 abstract "We prove that the 2-primary $pi_{61}$ is zero. As a consequence, the Kervaire invariant element $theta_5$ is contained in the strictly defined 4-fold Toda bracket $langle 2, theta_4, theta_4, 2rangle$. Our result has a geometric corollary: the 61-sphere has a unique smooth structure and it is the last odd dimensional case - the only ones are $S^1, S^3, S^5$ and $S^{61}$. Our proof is a computation of homotopy groups of spheres. A major part of this paper is to prove an Adams differential $d_3(D_3) = B_3$. We prove this differential by introducing a new technique based on the algebraic and geometric Kahn-Priddy theorems. The success of this technique suggests a theoretical way to prove Adams differentials in the sphere spectrum inductively by use of differentials in truncated projective spectra." @default.
- W2611750399 created "2017-05-12" @default.
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- W2611750399 date "2016-01-10" @default.
- W2611750399 modified "2023-09-23" @default.
- W2611750399 title "The triviality of the 61-stem in the stable homotopy groups of spheres" @default.
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- W2611750399 doi "https://doi.org/10.48550/arxiv.1601.02184" @default.
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