---
date: 2022-02-23 18:45
modification date: Wednesday 23rd February 2022 18:45:08
title: "equivariant stable homotopy theory"
aliases: [equivariant stable homotopy theory]

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


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- Tags 
	- #todo/untagged
- Refs:
	- [attachments/Equivariant Stable Homotopy Theory 1.pdf](attachments/Equivariant%20Stable%20Homotopy%20Theory%201.pdf) #resources/notes 
	- [https://www.msri.org/summer_schools/747](https://www.msri.org/summer_schools/747) #resources/workshops 
	- Schwede lecture notes: <https://people.math.rochester.edu/faculty/doug/otherpapers/schwede-eqv.pdf#page=1> #resources/notes 

- Links:
	- #todo/create-links 

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# equivariant stable homotopy theory


# Topics

- Special functors:
	- [Mackey functor](Mackey%20functor.md)
	- [Tambara functors](Tambara%20functors)
	- [Green functor](Green%20functor)
	- [lax functor](lax%20functor.md)
- [transfer](Unsorted/transfers.md)
	- [norm map](Unsorted/homotopy%20fixed%20points.md) (multiplicative transfer)
	- [trace map](trace%20map) (additive transfer)
	- [Burnside ring (homotopy theory)](Burnside%20ring%20(homotopy%20theory).md)
- [Box product](Box%20product)
- [representation ring](representation%20ring.md)
- [coend](coend.md)
- [Factorization homology](Factorization%20homology.md)

# Misc


Cheng's theorems: uses the [norm map](norm%20map), [Atiyah duality](Atiyah%20duality), and the [Adams isomorphism](Adams%20isomorphism).
![](attachments/Pasted%20image%2020220325232019.png)

Poincare duality for [Morava K theory](Unsorted/Morava%20K%20theory.md):
![](attachments/Pasted%20image%2020220325232114.png)
![](attachments/Pasted%20image%2020220325232128.png)