---
date: 2022-02-23 18:45
modification date: Friday 18th March 2022 13:51:19
title: Steenrod algebra
aliases: [Steenrod operations, Steenrod]

---


---

- Tags 
	- #homotopy/stable-homotopy 
- Refs:
	- <https://link.springer.com/content/pdf/10.1007%2F978-3-319-23488-5_4.pdf#page=7>
- Links:
	- [spectra](Unsorted/spectra.md)
	- [spectral sequence](Unsorted/spectral%20sequence.md)
	- [Adams Sseq](Archive/0200_Stable%20Homotopy%20Seminar%202021/Adams%20Sseq.md)
	- [koszul duality](Unsorted/koszul%20duality.md)
	- [Hopf invariant one](Unsorted/Hopf%20invariant%20one.md)
	- [Thom spectra](Unsorted/Pontrayagin-Thom.md)

---

# Steenrod algebra

![](attachments/Pasted%20image%2020220508174954.png)

![](attachments/Pasted%20image%2020220508175126.png)

![](attachments/Pasted%20image%2020220508174932.png)

![](attachments/Pasted%20image%2020220209185147.png)

![](attachments/Pasted%20image%2020220318135117.png)

![](attachments/Pasted%20image%2020220508174919.png)
# Actions

![](attachments/Pasted%20image%2020220325233150.png)

# Stability
![](attachments/Pasted%20image%2020220403213955.png)
![](attachments/Pasted%20image%2020220403214014.png)


# Hopf algebra structure
![](attachments/Pasted%20image%2020220508175217.png)

![](attachments/Pasted%20image%2020220404090929.png)

# Examples

See [example computations of Steenrod operations](example%20computations%20of%20Steenrod%20operations.md).


# Wu Formula

See [Stiefel-Whitney](Unsorted/Stiefel-Whitney%20class.md) classes:
![](attachments/Pasted%20image%2020220508182126.png)