This paper proves that the element h_6^2 is a permanent cycle in the Adams spectral sequence, thereby establishing the existence of framed manifolds of Kervaire invariant one in dimension 126 and resolving the Kervaire invariant problem.
Classical stable homotopy groups of spheres via $\mathbb{F}_2$-synthetic methods
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abstract
We study the $\mathbb{F}_2$-synthetic Adams spectral sequence. We obtain new computational information about $\mathbb{C}$-motivic and classical stable homotopy groups.
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On the Last Kervaire Invariant Problem
This paper proves that the element h_6^2 is a permanent cycle in the Adams spectral sequence, thereby establishing the existence of framed manifolds of Kervaire invariant one in dimension 126 and resolving the Kervaire invariant problem.