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Max
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Question: Is there a group $G$ and a CW-complex $X$ such that

  1. $X$ is homotopy equivalent to the circle $S^{1}$.

  2. $G$ acts on $X$

  3. the space of fixed points $X^{G}$ is weakly equivalent to $S^{2}$ ?

Question: Is there a group $G$ and a CW-complex $X$ such that

  1. $X$ is homotopy equivalent to the circle $S^{1}$.

  2. $G$ acts on $X$

  3. the space fixed points $X^{G}$ is weakly equivalent to $S^{2}$ ?

Question: Is there a group $G$ and a CW-complex $X$ such that

  1. $X$ is homotopy equivalent to the circle $S^{1}$.

  2. $G$ acts on $X$

  3. the space of fixed points $X^{G}$ is weakly equivalent to $S^{2}$ ?

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Max
Max
  • 1.6k
  • 11
  • 21

from a circle to higher spheres

Question: Is there a group $G$ and a CW-complex $X$ such that

  1. $X$ is homotopy equivalent to the circle $S^{1}$.

  2. $G$ acts on $X$

  3. the space fixed points $X^{G}$ is weakly equivalent to $S^{2}$ ?