Contents

group theory

spin geometry

string geometry

# Contents

## Idea

The group $Spin(2)$ is the spin group in 2 dimensions, hence the double cover of SO(2)

$\array{ \mathbb{Z}/2 &\hookrightarrow& Spin(2) \\ && \downarrow \\ && SO(2) }$

In fact there is an isomorphism $Spin(2) \simeq SO(2) \simeq U(1)$ with the circle group which exhibits the above as the real Hopf fibration

$\array{ \mathbb{Z}/2 &\hookrightarrow& S^1 \\ && \downarrow^{\mathrlap{\cdot 2}} \\ && S^1 }$

Last revised on March 22, 2019 at 09:13:08. See the history of this page for a list of all contributions to it.