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Oliver
Oliver
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I have been stuck for some time, thinking about the following question.

Let $G$ be a Lie group. Its classifying space $BG$ can be seen as the differentiable stack $[pt/G]$, which is of dimension $-dim(G)$.

Can something similar be said for the based loop group $\Omega G$ of pointed maps from $S^1$ to $G$ ?

I mean, is $\Omega G$ a differentiable stack and, if so, what is its dimension?

Best,

O.

I have been stuck for some time, thinking about the following question.

Let $G$ be a Lie group. Its classifying space $BG$ can be seen as the differentiable stack $[pt/G]$, which of dimension $-dim(G)$.

Can something similar be said for the based loop group $\Omega G$ of pointed maps from $S^1$ to $G$ ?

I mean, is $\Omega G$ a differentiable stack and, if so, what is its dimension?

Best,

O.

I have been stuck for some time, thinking about the following question.

Let $G$ be a Lie group. Its classifying space $BG$ can be seen as the differentiable stack $[pt/G]$, which is of dimension $-dim(G)$.

Can something similar be said for the based loop group $\Omega G$ of pointed maps from $S^1$ to $G$ ?

I mean, is $\Omega G$ a differentiable stack and, if so, what is its dimension?

Best,

O.

Source Link
Oliver
Oliver
  • 123
  • 7

Based loop groups as stacks?

I have been stuck for some time, thinking about the following question.

Let $G$ be a Lie group. Its classifying space $BG$ can be seen as the differentiable stack $[pt/G]$, which of dimension $-dim(G)$.

Can something similar be said for the based loop group $\Omega G$ of pointed maps from $S^1$ to $G$ ?

I mean, is $\Omega G$ a differentiable stack and, if so, what is its dimension?

Best,

O.