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Classification of all equivariant structure on the MobiousMöbius line bundles

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YCor
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Is therethere a classificationclassification of all equivariant structure of the Mobious lineequivariant structures of the Möbius line bundle  $\ell\to S^1$?.

For example the antipodal actionantipodal action of  $\mathbb{Z}/2\mathbb{Z}$ on $S^1$ can notcannot be lifted to the total space lifted to the total space $\ell$ toto get an equivariant structurean equivariant structure. But what about general casewhat about the general case?

In particularparticular, let  $\phi_{\theta}$ be the irrationalbe the irrational rotation of the circlethe circle by  $\theta$. Can the action of of $\mathbb{Z}$ onon $S^1$ bygiven by $n.x=\phi_{\theta}^n(x)$ be lifted tobe lifted to an action on the total spacespace of the Mobious bundle to givethe Möbius bundle to give us an equivariant bundlean equivariant bundle?

Is there a classification of all equivariant structure of the Mobious line bundle  $\ell\to S^1$?.

For example the antipodal action of  $\mathbb{Z}/2\mathbb{Z}$ on $S^1$ can not be lifted to the total space $\ell$ to get an equivariant structure. But what about general case?

In particular let  $\phi_{\theta}$ be the irrational rotation of the circle by  $\theta$. Can the action of $\mathbb{Z}$ on $S^1$ by $n.x=\phi_{\theta}^n(x)$ be lifted to an action on total space of the Mobious bundle to give us an equivariant bundle?

Is there a classification of all equivariant structures of the Möbius line bundle $\ell\to S^1$?.

For example the antipodal action of $\mathbb{Z}/2\mathbb{Z}$ on $S^1$ cannot be lifted to the total space $\ell$ to get an equivariant structure. But what about the general case?

In particular, let $\phi_{\theta}$ be the irrational rotation of the circle by $\theta$. Can the action of $\mathbb{Z}$ on $S^1$ given by $n.x=\phi_{\theta}^n(x)$ be lifted to an action on the total space of the Möbius bundle to give us an equivariant bundle?

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Ali Taghavi
Ali Taghavi
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Classification of all equivariant structure on the Mobious line bundlebundles

Is there a classification of all equivariant structure of the Mobious line bundle $\ell\to S^1$?.

For example the antipodal action of $\mathbb{Z}/2\mathbb{Z}$ on $S^1$ can not be lifted to the total space $\ell$ to get an equivariant structure. But what about general case?

In particular let $\phi_{\theta}$ be the irrational rotation of the circle by $\theta$. Can the action of $\mathbb{Z}$ on $S^1$ by $n.x=\phi_{\theta}^n(x)$ be lifted to an action on total space of the Mobious bundle to give us an equivariant bundle?

Classification of equivariant structure on the Mobious line bundle

Is there a classification of all equivariant structure of the Mobious line bundle $\ell\to S^1$?.

For example the antipodal action of $\mathbb{Z}/2\mathbb{Z}$ on $S^1$ can not be lifted to the total space to get an equivariant structure. But what about general case?

In particular let $\phi_{\theta}$ be the irrational rotation of the circle by $\theta$. Can the action of $\mathbb{Z}$ on $S^1$ by $n.x=\phi_{\theta}^n(x)$ be lifted to an action on total space of the Mobious bundle to give us an equivariant bundle?

Classification of all equivariant structure on the Mobious line bundles

Is there a classification of all equivariant structure of the Mobious line bundle $\ell\to S^1$?.

For example the antipodal action of $\mathbb{Z}/2\mathbb{Z}$ on $S^1$ can not be lifted to the total space $\ell$ to get an equivariant structure. But what about general case?

In particular let $\phi_{\theta}$ be the irrational rotation of the circle by $\theta$. Can the action of $\mathbb{Z}$ on $S^1$ by $n.x=\phi_{\theta}^n(x)$ be lifted to an action on total space of the Mobious bundle to give us an equivariant bundle?

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Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123