---
date: 2022-02-23 18:45
modification date: Sunday 3rd April 2022 19:18:24
title: "Serre spectral sequence"
aliases: [Serre spectral sequence, transgression]

---

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


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- Tags 
	- #spectral-sequences 
- Refs:
	- #todo/add-references
- Links:
	- [examples of spectral sequences](Unsorted/examples%20of%20spectral%20sequences.md)
	- [Euler class](Unsorted/Euler%20class.md)

---

# Serre spectral sequence

![](attachments/Pasted%20image%2020220422205642.png)

![](attachments/Pasted%20image%2020210613214604.png)
![](attachments/Pasted%20image%2020210613214639.png)

# Serre exact sequence

![](attachments/Pasted%20image%2020220403192546.png)
![](attachments/Pasted%20image%2020220403192556.png)
![](attachments/Pasted%20image%2020220403192637.png)

Proving the [Hurewicz](Unsorted/Hurewicz.md) theorem with the [Path Loop Fibration](To%20Review/Path%20Loop%20Fibration.md):
![](attachments/Pasted%20image%2020220403192724.png)



# Edge morphisms

Idea:
![](attachments/Pasted%20image%2020220403191649.png)


![](attachments/Pasted%20image%2020220403191342.png)

![](attachments/Pasted%20image%2020220403191349.png)

![](attachments/Pasted%20image%2020220403191619.png)

# Transgressions

![](attachments/Pasted%20image%2020220403191736.png)

![](attachments/Pasted%20image%2020220403192158.png)