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date: 2022-04-05 23:42
modification date: Friday 22nd April 2022 15:36:16
title: "complex bordism"
aliases: [complex bordism, MU, complex cobordism]
---

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

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- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
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# complex bordism

The complex bordism spectrum $\MU$ is a universal [cohomolology theories](cohomolology%20theories) : complex orientations of a spectrum $E$ are in one-to-one correspondence with multiplicative maps $\MU \to E$. 

- $\MU$ is a [Thom spectrum](Unsorted/Thom%20space.md)
![attachments/Pasted image 20210511204054.png](attachments/Pasted%20image%2020210511204054.png)

![](attachments/Pasted%20image%2020220425175711.png)


Relation to [complex bordism](Unsorted/complex%20bordism.md):
![](attachments/Pasted%20image%2020220422153551.png)