On the non-existence of elements of Kervaire invariant one — mentioned by robinhouston

Mon, 05 May 2025 22:58:41 GMT

The proof that it stops instead of going on forever is here: https://arxiv.org/abs/0908.3724 It’s more than 200 pages of pretty technical mathematics, so I’m reasonably confident that there is no description a layperson might understand.

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On the non-existence of elements of Kervaire invariant one — mentioned by aleph_minus_one

Mon, 05 May 2025 22:48:46 GMT

> They’re all double the last dimension plus two, without skipping any in that sequence - but that offers no insight into why it wouldn’t hold for 254. Wikipedia at least gives a literature reference and concise explanation for the reason: > https://en.wikipedia.org/w/index.php?title=Kervaire_invarian... "Hill, Hopkins & Ravenel (2016) showed that the Kervaire invariant is zero for n-dimensional framed manifolds for n = 2^k− 2 with k ≥ 8. They constructed a cohomology theory Ω with the following properties from which their result follows immediately: * The coefficient groups Ω^n(point) have…

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On the non-existence of elements of Kervaire invariant one · HackerPapers discussions

On the non-existence of elements of Kervaire invariant one — mentioned by robinhouston

On the non-existence of elements of Kervaire invariant one — mentioned by aleph_minus_one