---
date: 2021-05-02
tags: [ web/quick-notes ]
---


# 2021-05-02

## [Hopf Invariant One](Hopf%20Invariant%20One.md)

- Cool fact: you can show the non-existence of [Hopf invariant one](Hopf%20invariant%20one.md) elements in dimensions $1,2,4,8$ using [K-theory](K-theory.md). 
- The argument is pretty clean, and the paper is only 8 pages: 
	- <https://www.maths.ed.ac.uk/~v1ranick/papers/adamatiy.pdf>

- See Mosh-Tang for the original proof using [cohomology operations](cohomology%20operations.md) : <https://www.maths.ed.ac.uk/~v1ranick/papers/moshtang.pdf>.
	- This also apparently includes computations of cohomology of [Eilenberg-MacLane spaces](Eilenberg-MacLane%20spaces.md).