---
date: 2022-02-23 18:45
modification date: Wednesday 23rd February 2022 18:45:08
title: "spectral sequence"
aliases: [spectral sequence]

---

Last modified date: <%+ tp.file.last_modified_date() %>


---

- Tags 
	- #spectral-sequences 
- Refs:
	- Spectral sequence paper:
		 - [attachments/Combined SS Calculation Paper 1.pdf](attachments/Combined%20SS%20Calculation%20Paper%201.pdf)
		- [attachments/SS Calculation Paper.pdf](attachments/SS%20Calculation%20Paper.pdf)
- Links:
	- [Serre spectral sequence](Unsorted/Serre%20spectral%20sequence.md)
	- [Adams spectral sequence](Archive/0200_Stable%20Homotopy%20Seminar%202021/Adams%20Sseq.md)
	- [Atiyah Hirzebruch spectral sequence](Atiyah%20Hirzebruch%20spectral%20sequence.md)
	- [Adams-Novikov spectral sequence](Adams-Novikov%20spectral%20sequence)
	- [examples of spectral sequences](Unsorted/examples%20of%20spectral%20sequences.md)
	- [EHP sequence](EHP%20sequence.md)
	- [Bousfield localization](Unsorted/Bousfield%20localization.md)
	- [motivation for spectral sequences](Unsorted/motivation%20for%20spectral%20sequences.md)

---

# spectral sequence


![](attachments/Pasted%20image%2020220408004636.png)

![](attachments/Pasted%20image%2020220408004732.png)
![](attachments/Pasted%20image%2020220408004740.png)
![](attachments/Pasted%20image%2020220408004755.png)
![](attachments/Pasted%20image%2020220408004804.png)
![](attachments/Pasted%20image%2020220408004834.png)


# From a filtration

![](attachments/Pasted%20image%2020220408200934.png)
![](attachments/Pasted%20image%2020220408201014.png)

## Example: symmetric group $S_3$

![](attachments/Pasted%20image%2020220408004913.png)
![](attachments/Pasted%20image%2020220408004920.png)
![](attachments/Pasted%20image%2020220408004931.png)

## Example: infinite dihedral groups $D_\infty \cong C_2^{\ast_2}$

![](attachments/Pasted%20image%2020220408005018.png)
![](attachments/Pasted%20image%2020220408005030.png)

![](attachments/Pasted%20image%2020220408005040.png)