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For questions about spin manifolds, the groups $\operatorname{Spin}(n)$, as well as generalisations such as $\operatorname{Pin}^{\pm}(n)$ and $\operatorname{Spin}^c(n)$. This tag should also be used for any questions about the geometry of spin manifolds, including questions involving Dirac operators and the Lichnerowicz formula.

22 votes

Triality of Spin(8)

Here's my favorite way to answer your question. Hopefully the answer to Robert Bryant's question is "yes". Let $A$ be the ring of octonions (the "nonsplit" octonions over ${\mathbb R}$); it comes wi …
Marty's user avatar
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