# 2021-05-02

## Hopf Invariant One

• Cool fact: you can show the non-existence of Hopf invariant one elements in dimensions $$1,2,4,8$$ using K-theory.
• The argument is pretty clean, and the paper is only 8 pages:
• See Mosh-Tang for the original proof using cohomology operations : https://www.maths.ed.ac.uk/~v1ranick/papers/moshtang.pdf.
• This also apparently includes computations of cohomology of Eilenberg-MacLane spaces.
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