---
date: 2022-02-23 18:45
modification date: Wednesday 23rd February 2022 18:45:08
title: "characteristic class"
aliases: [characteristic classes]

---

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


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- Tags 
	- #todo/untagged
- Refs:
	- Milnor-Stasheff
- Links:
	- [Euler class](Euler%20class.md) 
		- or Euler bundle..? Find in old email.
		- [Poincare-Hopf index theorem](Poincare-Hopf%20index%20theorem)
	- [Chern class](Chern%20class.md)
	- [Stiefel-Whitney class](Stiefel-Whitney%20class.md)
	- [Pontrayagin class](Pontrayagin%20class.md)

---

# characteristic class

![](attachments/Pasted%20image%2020220403210723.png)

# Results

Characteristic classes are elements of $H^*(\B G)$, the cohomology of [classifying space](classifying%20space.md) .

This can be used to define characteristic classes for [bundle](bundle).

![](attachments/Pasted%20image%2020210613124812.png)
![](attachments/Pasted%20image%2020220408204138.png)

# Orbifolds
See [orbifold](Unsorted/orbifold.md).

![](attachments/Pasted%20image%2020220213020542.png)