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Max Schattman
Max Schattman
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Compact Lie groups are a very special type of compact group, namely those which admit a differentiable structure. Is it possible to describe compact Lie groups in purely topological terms, that is, those there exist a topological property $X$, such that a compact group $G$ is Lie IFF it satisfies $X$? I recall hearing that $X$ can be given in terms of connectedness . . . but can't find a mention of this in the literature.

Compact Lie groups are a very special type of compact group, namely those which admit a differentiable structure. Is it possible to describe compact Lie groups in purely topological terms, that is, those there exist a topological property $X$, such that a compact group $G$ is Lie IFF it satisfies $X$?

Compact Lie groups are a very special type of compact group, namely those which admit a differentiable structure. Is it possible to describe compact Lie groups in purely topological terms, that is, those there exist a topological property $X$, such that a compact group $G$ is Lie IFF it satisfies $X$? I recall hearing that $X$ can be given in terms of connectedness . . . but can't find a mention of this in the literature.

Source Link
Max Schattman
Max Schattman
  • 993
  • 4
  • 13

Describing compact Lie groups in purely topological terms

Compact Lie groups are a very special type of compact group, namely those which admit a differentiable structure. Is it possible to describe compact Lie groups in purely topological terms, that is, those there exist a topological property $X$, such that a compact group $G$ is Lie IFF it satisfies $X$?