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Dimension 126 Contains Twisted Shapes, Mathematicians Prove
A new proof represents the culmination of a 65-year-old story about anomalous shapes in special dimensions.
In 2009, “to stem the tide of oblivion,” the mathematician Victor Snaith wrote a book exploring the implications of having manifolds with Kervaire invariant 1 in all the dimensions on Browder’s list. Since 1958, they’ve been organizing information about the structure of stable homotopy groups into an enormous but unfinished atlas of dots called the Adams spectral sequence. Recently, Xu and Robert Burklund of the University of Copenhagen figured out that a handful of special dimensions seem to exhibit another kind of oddball behavior in the third row of the atlas.
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