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Gerry Myerson
Gerry Myerson
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Does there exist smooth cirlcecircle action on manifolds M^{4n} with exactly three fixed points such that n\neq 1

I have a question in mind for some time. That is, does there exist a smooth circle action on a closed manifold M^{4n} $M^{4n}$ (n\geq 2$n\geq 2$) with exactly three fixed points? RemmarksRemarks:(1)For For n=1, the examples are obvious (standard linear circle action on CP^2$CP^2$). (2)If If a manifold admits a circle action with 3 fixed points, then the signature of this manifold is 1, so the dimension of this manifold is necessarily divisible by 4.

Does there exist smooth cirlce action on manifolds M^{4n} with exactly three fixed points such that n\neq 1

I have a question in mind for some time. That is, does there exist a smooth circle action on a closed manifold M^{4n} (n\geq 2) with exactly three fixed points? Remmarks:(1)For n=1, the examples are obvious (standard linear circle action on CP^2). (2)If a manifold admits a circle action with 3 fixed points, then the signature of this manifold is 1, so the dimension of this manifold is necessarily divisible by 4.

Does there exist smooth circle action on manifolds M^{4n} with exactly three fixed points such that n\neq 1

I have a question in mind for some time. That is, does there exist a smooth circle action on a closed manifold $M^{4n}$ ($n\geq 2$) with exactly three fixed points? Remarks:(1) For n=1, the examples are obvious (standard linear circle action on $CP^2$). (2) If a manifold admits a circle action with 3 fixed points, then the signature of this manifold is 1, so the dimension of this manifold is necessarily divisible by 4.

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Does there exist smooth circlecirlce action on manifolds M^{4n} with exactly three fixed points such that n\neq 1

I have a question in mind for some time. That is, does there exist a smooth circle action on a closed manifold $M^{4n}$M^{4n} ($n\geq 2$n\geq 2) with exactly three fixed points? RemarksRemmarks:(1) ForFor n=1, the examples are obvious (standard linear circle action on $CP^2$CP^2). (2) IfIf a manifold admits a circle action with 3 fixed points, then the signature of this manifold is 1, so the dimension of this manifold is necessarily divisible by 4.

Does there exist smooth circle action on manifolds M^{4n} with exactly three fixed points such that n\neq 1

I have a question in mind for some time. That is, does there exist a smooth circle action on a closed manifold $M^{4n}$ ($n\geq 2$) with exactly three fixed points? Remarks:(1) For n=1, the examples are obvious (standard linear circle action on $CP^2$). (2) If a manifold admits a circle action with 3 fixed points, then the signature of this manifold is 1, so the dimension of this manifold is necessarily divisible by 4.

Does there exist smooth cirlce action on manifolds M^{4n} with exactly three fixed points such that n\neq 1

I have a question in mind for some time. That is, does there exist a smooth circle action on a closed manifold M^{4n} (n\geq 2) with exactly three fixed points? Remmarks:(1)For n=1, the examples are obvious (standard linear circle action on CP^2). (2)If a manifold admits a circle action with 3 fixed points, then the signature of this manifold is 1, so the dimension of this manifold is necessarily divisible by 4.

fixed some typos, improved formatting
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Gerry Myerson
Gerry Myerson
  • 39.9k
  • 10
  • 186
  • 247

Does there exist smooth cirlcecircle action on manifolds M^{4n} with exactly three fixed points such that n\neq 1

I have a question in mind for some time. That is, does there exist a smooth circle action on a closed manifold M^{4n} $M^{4n}$ (n\geq 2$n\geq 2$) with exactly three fixed points? RemmarksRemarks:(1)For For n=1, the examples are obvious (standard linear circle action on CP^2$CP^2$). (2)If If a manifold admits a circle action with 3 fixed points, then the signature of this manifold is 1, so the dimension of this manifold is necessarily divisible by 4.

Does there exist smooth cirlce action on manifolds M^{4n} with exactly three fixed points such that n\neq 1

I have a question in mind for some time. That is, does there exist a smooth circle action on a closed manifold M^{4n} (n\geq 2) with exactly three fixed points? Remmarks:(1)For n=1, the examples are obvious (standard linear circle action on CP^2). (2)If a manifold admits a circle action with 3 fixed points, then the signature of this manifold is 1, so the dimension of this manifold is necessarily divisible by 4.

Does there exist smooth circle action on manifolds M^{4n} with exactly three fixed points such that n\neq 1

I have a question in mind for some time. That is, does there exist a smooth circle action on a closed manifold $M^{4n}$ ($n\geq 2$) with exactly three fixed points? Remarks:(1) For n=1, the examples are obvious (standard linear circle action on $CP^2$). (2) If a manifold admits a circle action with 3 fixed points, then the signature of this manifold is 1, so the dimension of this manifold is necessarily divisible by 4.

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