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I want to learn about the $2$-primary component of the stable homotopy groups of spheres in dimension $64$. Since the triviality of $61$-st stem has been proved just recently, I thought that either I am unable to find about ${_2\pi_{64}^s}$ or still there is something unknown about this. I did not find anything in Ravenel's Green book about his, and not sure if there is anything in Toda's book? I will be very grateful for any advise on this!?!

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An answer is given in Theorem 3.5 'On the computation of stable stems' by Kochman and Mahowald. In light of the recent work of Isaksen, Xu, Wang and others, I'm not sure how reliable this result is.

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  • $\begingroup$ @Drew Heard Do you mean the results themselves could affect computations of Kochman and Mahowald, or do you mean that the methods employed by Isaken, Wang, Xu, and others could result in a different result for the $64$-th stem? $\endgroup$ – user51223 Dec 1 '17 at 19:35
  • $\begingroup$ @user51223 See the bottom of page 4 of arxiv.org/pdf/1407.8418.pdf - there are some inconsistencies with the latest calculations and the Kochman/Mahowald calculations. Thus, I'm not sure if the calculation in the 64 stem is correct. $\endgroup$ – Drew Heard Dec 2 '17 at 10:23
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This is the result from Kochman and Mahowald:

  

Which you can get from "On the Computation of Stable Stems", Contemporary Mathematics Volume 181, 1995.

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