--- date: 2022-01-10 09:52 modification date: Friday 18th March 2022 13:52:18 title: Adams Sseq aliases: [Adams spectral sequence, AdSS, AdSSeq] created: 2023-04-17T14:54 updated: 2023-04-17T14:56 --- --- - Tags: - #homotopy/stable-homotopy - Refs: - Bruner [An Adams Spectral Sequence Primer](http://www.rrb.wayne.edu/papers/adams.pdf) #resources/notes - [Rognes, Spectral sequences]https://www.uio.no/studier/emner/matnat/math/MAT9580/v21/dokumenter/spseq.pdf) #resources/books - McLeary, [A User's Guide to Spectral Sequences](https://people.math.rochester.edu/faculty/doug/otherpapers/McCleary-UGSS.pdf) #resources/books - Adams, [Non-existence of elements of Hopf invariant one](https://www.maths.ed.ac.uk/~v1ranick/papers/adams1.pdf) #resources/papers - Steenrod [Cohomology Operations](https://people.math.rochester.edu/faculty/doug/otherpapers/steenrod-epstein.pdf) #resources/books - Ravenel, *Complex cobordism and stable homotopy groups of spheres* #resources/books - #resources/notes - Construction of the spectral sequence: - Links: - [Steenrod algebra](Unsorted/Steenrod%20algebra.md) - [spectra](Unsorted/spectra.md) - [completion](Unsorted/adic%20completion.md) --- # The Adams spectral sequence ![](attachments/Pasted%20image%2020220508184258.png) ![](attachments/Pasted%20image%2020220318135234.png) Using [koszul duality](Unsorted/koszul%20duality.md) to compute [stable homotopy groups of spheres](Unsorted/stable%20homotopy%20groups%20of%20spheres.md): ![](attachments/Pasted%20image%2020220318135407.png) ![](attachments/Pasted%20image%2020220508183209.png) ![](attachments/Pasted%20image%2020220508183254.png) ![](attachments/Pasted%20image%2020220508183350.png) ![](attachments/Pasted%20image%2020220508211134.png) ![](attachments/Pasted%20image%2020220508211225.png) ![](attachments/Pasted%20image%2020220508211749.png) # Solving extensions ![](attachments/Pasted%20image%2020220508211434.png) # Misc The main calculation tool in [stable homotopy](stable%20homotopy.md): ![](2023-04-17-9.png)