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Peter May
Peter May
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I'm feeling mischievous. The history of the Kervaire invariant problem is strewn with false proofs, Jim Milgram's is only one of many. A student of mine (who I will leave nameless) had a preprint (around 1980?) that solved the problem but that Mark Mahowald quickly shot down. The most recent example I know of is that of a Russian mathematician (who I will also leave nameless). See Math Reviews MR2590025 (2010k:55031) Differentials of the Adams spectral sequence and the Kervaire invariant (Russian) Dokl. Akad. Nauk 427 (2009), no. 5, 601–604; translation in Dokl. Math. 80 (2009), no. 1, 573–576. From the text (translated from the Russian): "In this paper, we study the differentials of the Adams spectral sequence for stable homotopy groups of spheres and solve the Kervaire invariant one problem for n-dimensional manifolds when $n=2^i-2$, $i\geq 6$." That is a four page paper. Would that it were so simple!

I'm feeling mischievous. The history of the Kervaire invariant problem is strewn with false proofs, Jim Milgram's is only one of many. A student of mine (who I will leave nameless) had a preprint (around 1980?) that solved the problem but that Mark Mahowald quickly shot down. The most recent example I know of is that of a Russian mathematician (who I will also leave nameless). See Math Reviews MR2590025 (2010k:55031) Differentials of the Adams spectral sequence and the Kervaire invariant (Russian) Dokl. Akad. Nauk 427 (2009), no. 5, 601–604; translation in Dokl. Math. 80 (2009), no. 1, 573–576. From the text (translated from the Russian): "In this paper, we study the differentials of the Adams spectral sequence for stable homotopy groups of spheres and solve the Kervaire invariant one problem for n-dimensional manifolds when $n=2^i-2$, $i\geq 6$. That is a four page paper. Would that it were so simple!

I'm feeling mischievous. The history of the Kervaire invariant problem is strewn with false proofs, Jim Milgram's is only one of many. A student of mine (who I will leave nameless) had a preprint (around 1980?) that solved the problem but that Mark Mahowald quickly shot down. The most recent example I know of is that of a Russian mathematician (who I will also leave nameless). See Math Reviews MR2590025 (2010k:55031) Differentials of the Adams spectral sequence and the Kervaire invariant (Russian) Dokl. Akad. Nauk 427 (2009), no. 5, 601–604; translation in Dokl. Math. 80 (2009), no. 1, 573–576. From the text (translated from the Russian): "In this paper, we study the differentials of the Adams spectral sequence for stable homotopy groups of spheres and solve the Kervaire invariant one problem for n-dimensional manifolds when $n=2^i-2$, $i\geq 6$." That is a four page paper. Would that it were so simple!

Source Link
Peter May
Peter May
  • 30.4k
  • 3
  • 96
  • 140

I'm feeling mischievous. The history of the Kervaire invariant problem is strewn with false proofs, Jim Milgram's is only one of many. A student of mine (who I will leave nameless) had a preprint (around 1980?) that solved the problem but that Mark Mahowald quickly shot down. The most recent example I know of is that of a Russian mathematician (who I will also leave nameless). See Math Reviews MR2590025 (2010k:55031) Differentials of the Adams spectral sequence and the Kervaire invariant (Russian) Dokl. Akad. Nauk 427 (2009), no. 5, 601–604; translation in Dokl. Math. 80 (2009), no. 1, 573–576. From the text (translated from the Russian): "In this paper, we study the differentials of the Adams spectral sequence for stable homotopy groups of spheres and solve the Kervaire invariant one problem for n-dimensional manifolds when $n=2^i-2$, $i\geq 6$. That is a four page paper. Would that it were so simple!