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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 13th 2016
   • (edited May 13th 2016)
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   Author: Urs
   Format: MarkdownItexMight anyone have a pdf copy of Peter May's thesis for me, the document that, I gather, expands over the published version [May 66](https://ncatlab.org/nlab/show/May+spectral+sequence#May66) by a discussion specific to the Steenrod algebra?

   Might anyone have a pdf copy of Peter May’s thesis for me, the document that, I gather, expands over the published version May 66 by a discussion specific to the Steenrod algebra?

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 13th 2016
   • (edited May 13th 2016)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have been adding to _[[May spectral sequence]]_ details of its construction, following the sketch on p. 69 of [[Complex cobordism and stable homotopy groups of spheres|Ravenel 86]] (also [Kochman 96, section 5.3](https://ncatlab.org/nlab/show/May%20spectral%20sequence#Kochman96)). I have tried to make it very explicit, and will eventually try to make it more expository. There might still be glitches, though. I have marked the entry as "under construction".

   I have been adding to May spectral sequence details of its construction, following the sketch on p. 69 of Ravenel 86 (also Kochman 96, section 5.3).

   I have tried to make it very explicit, and will eventually try to make it more expository. There might still be glitches, though. I have marked the entry as “under construction”.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 13th 2016
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have now also started to add the discussion [here](https://ncatlab.org/nlab/show/May+spectral+sequence#TheSecondPageOfTheClassicalAdamsSpectralSequence) of how from the May spectral sequence the homotopy groups of spheres at 2 are computed. For the moment I tried to put in just enough information to make clear how the computation works. And then the tables.

   I have now also started to add the discussion here of how from the May spectral sequence the homotopy groups of spheres at 2 are computed. For the moment I tried to put in just enough information to make clear how the computation works. And then the tables.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 19th 2016
   • (edited Jul 19th 2016)
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   Author: Urs
   Format: MarkdownItexOn the first page of the May spectral sequence for the second page of the classical Adams spectral sequence: how do we deduce that all $(h_{n,k})^2$ are $d_1$-cocycles? In Kochman's [[Bordism, Stable Homotopy and Adams Spectral Sequences|book]] on p. 201 it says "since $d_1$ is a derivation". But the product is in the cobar complex, where we don't have that $(d_1 h_{n,k}) h_{n,k} + h_{n,k} (d_1 h_{n,k}) = 2 h_{n,k} (d_1 h_{n,k})$ (hence $\cdots = 0 \;mod \;2$). Or do we? I must be missing something here. [edit: got it; the product of course takes place not in the cobar complex, but in its image in the $E_1$-page, which is graded commutative]

   On the first page of the May spectral sequence for the second page of the classical Adams spectral sequence: how do we deduce that all $(h_{n,k})^2$ are $d_1$-cocycles? In Kochman’s book on p. 201 it says “since $d_1$ is a derivation”. But the product is in the cobar complex, where we don’t have that $(d_1 h_{n,k}) h_{n,k} + h_{n,k} (d_1 h_{n,k}) = 2 h_{n,k} (d_1 h_{n,k})$ (hence $\cdots = 0 \;mod \;2$). Or do we? I must be missing something here.

   [edit: got it; the product of course takes place not in the cobar complex, but in its image in the $E_1$-page, which is graded commutative]