Skip to main content
MathOverflow

Return to Question

added 15 characters in body
Source Link
aglearner
aglearner
  • 14.3k
  • 8
  • 40
  • 99

Question 1. Is there a classification of smooth $S^1$-actions with isolated fixed points on the standard $\mathbb CP^3$?

Question 2. What if one additionally imposes the condition that the action preserves an almost complex structure homotopic to the standard one? (here we consider almost complex structures up to homotopies through $S^1$-invariant almost complex structures).

Note that non-linear actions on $\mathbb CP^3$ do exist, as is proved by Ted Petrie, see for example section 4:

Smooth $S^1$ actions on homotopy complex projective spaces and related topics http://www.ams.org/journals/bull/1972-78-02/S0002-9904-1972-12898-2/

I tried to check the articles that cite this article, but was not able to understand if the answer to my question isquestions are known.

Question 1. Is there a classification of smooth $S^1$-actions with isolated fixed points on the standard $\mathbb CP^3$?

Question 2. What if one additionally imposes the condition that the action preserves an almost complex structure homotopic to the standard one? (here we consider almost complex structures up to homotopies through $S^1$-invariant almost complex structures).

Note that non-linear actions on $\mathbb CP^3$ do exist, as is proved by Ted Petrie, see for example:

Smooth $S^1$ actions on homotopy complex projective spaces and related topics http://www.ams.org/journals/bull/1972-78-02/S0002-9904-1972-12898-2/

I tried check the articles that cite this article, but was not able to understand if the answer to my question is known.

Question 1. Is there a classification of smooth $S^1$-actions with isolated fixed points on the standard $\mathbb CP^3$?

Question 2. What if one additionally imposes the condition that the action preserves an almost complex structure homotopic to the standard one? (here we consider almost complex structures up to homotopies through $S^1$-invariant almost complex structures).

Note that non-linear actions on $\mathbb CP^3$ do exist, as is proved by Ted Petrie, see for example section 4:

Smooth $S^1$ actions on homotopy complex projective spaces and related topics http://www.ams.org/journals/bull/1972-78-02/S0002-9904-1972-12898-2/

I tried to check the articles that cite this article, but was not able to understand if the answer to my questions are known.

added 417 characters in body
Source Link
aglearner
aglearner
  • 14.3k
  • 8
  • 40
  • 99

Question 1. Is there a classification of smooth $S^1$-actions with isolated fixed points on the standard $\mathbb CP^3$?

Question 2. What if one additionally imposes the condition that the action preserves an almost complex structure homotopic to the standard one? (here we consider almost complex structures up to homotopies through $S^1$-invariant almost complex structures).

Note that non-linear actions on $\mathbb CP^3$ do exist, as is proved by Ted Petrie, see for example:

Smooth $S^1$ actions on homotopy complex projective spaces and related topics http://www.ams.org/journals/bull/1972-78-02/S0002-9904-1972-12898-2/

I tried check the articles that cite this article, but was not able to understand if the answer to my question is known.

Is there a classification of smooth $S^1$-actions with isolated fixed points on the standard $\mathbb CP^3$?

What if one additionally imposes the condition that the action preserves an almost complex structure homotopic to the standard one? (here we consider almost complex structures up to homotopies through $S^1$-invariant almost complex structures).

Question 1. Is there a classification of smooth $S^1$-actions with isolated fixed points on the standard $\mathbb CP^3$?

Question 2. What if one additionally imposes the condition that the action preserves an almost complex structure homotopic to the standard one? (here we consider almost complex structures up to homotopies through $S^1$-invariant almost complex structures).

Note that non-linear actions on $\mathbb CP^3$ do exist, as is proved by Ted Petrie, see for example:

Smooth $S^1$ actions on homotopy complex projective spaces and related topics http://www.ams.org/journals/bull/1972-78-02/S0002-9904-1972-12898-2/

I tried check the articles that cite this article, but was not able to understand if the answer to my question is known.

Source Link
aglearner
aglearner
  • 14.3k
  • 8
  • 40
  • 99

A classification of smooth $S^1$-actions on $\mathbb CP^3$?

Is there a classification of smooth $S^1$-actions with isolated fixed points on the standard $\mathbb CP^3$?

What if one additionally imposes the condition that the action preserves an almost complex structure homotopic to the standard one? (here we consider almost complex structures up to homotopies through $S^1$-invariant almost complex structures).