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Noel Lundström
Noel Lundström
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Noel Lundström
Noel Lundström
  • 363
  • 2
  • 8

Title. For what topological groups $G$ can we take $EG \rightarrow BG$ to be of the form $S^{\infty} \rightarrow BG$?

If $G$ is a subgroup of either $S^0,S^1,S^3$ or $S^7$ this induces a free action on $S^{\infty}$ and thus a $G-$principal bundle $S^{\infty} \rightarrow BG$. Does the reverse direction hold? That is, if $G$ acts freely on $S^{\infty}$ is it contained in some of the $S^0,S^1,...,S^7$ as a subgroup such that the induced action on $S^{\infty}$ is the same?

Title. For what topological groups $G$ can we take $EG \rightarrow BG$ to be of the form $S^{\infty} \rightarrow BG$?

If $G$ is a subgroup of either $S^0,S^1,S^3$ or $S^7$ this induces a free action on $S^{\infty}$ and thus a $G-$principal bundle $S^{\infty} \rightarrow BG$. Does the reverse direction hold? That is, if $G$ acts freely on $S^{\infty}$ is it contained in some of the $S^0,S^1,...,S^7$ as a subgroup such that the induced action is the same?

Title. For what topological groups $G$ can we take $EG \rightarrow BG$ to be of the form $S^{\infty} \rightarrow BG$?

If $G$ is a subgroup of either $S^0,S^1,S^3$ or $S^7$ this induces a free action on $S^{\infty}$ and thus a $G-$principal bundle $S^{\infty} \rightarrow BG$. Does the reverse direction hold? That is, if $G$ acts freely on $S^{\infty}$ is it contained in some of the $S^0,S^1,...,S^7$ as a subgroup such that the induced action on $S^{\infty}$ is the same?

Source Link
Noel Lundström
Noel Lundström
  • 363
  • 2
  • 8

For what topological groups $G$ can we take $EG \rightarrow BG$ to be of the form $S^{\infty} \rightarrow BG$?

Title. For what topological groups $G$ can we take $EG \rightarrow BG$ to be of the form $S^{\infty} \rightarrow BG$?

If $G$ is a subgroup of either $S^0,S^1,S^3$ or $S^7$ this induces a free action on $S^{\infty}$ and thus a $G-$principal bundle $S^{\infty} \rightarrow BG$. Does the reverse direction hold? That is, if $G$ acts freely on $S^{\infty}$ is it contained in some of the $S^0,S^1,...,S^7$ as a subgroup such that the induced action is the same?