# Tagged Questions

**16**

votes

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### Conceptual explanation for the relationship between Clifford algebras and KO

Recall the following table of Clifford algebras:
$$\begin{array}{ccc}
n & Cl_n & M_n/i^{*}M_{n+1}\\
1 & \mathbb{C} & \mathbb{Z}/2\mathbb{Z} \\
2 & \mathbb{H} & ...

**15**

votes

**3**answers

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### How do you relate the number of independent vector fields on spheres and Bott Periodicity for real K-Theory?

The theory of Clifford algebras gives us an explicit lower bound for the number of linearly independent vector fields on the $n$-sphere, and Adams proved that this is actually always the best ...