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Jonathan Beardsley
Jonathan Beardsley
12:06 AM
Does anyone know the homotopy type of the fiber of the multiplication by $p$ map from $CP^\infty$ to itself?
Haha, I guess this is pretty basic... I should try thinking before typing.
 
 
12 hours later…
Achim Krause
Achim Krause
12:12 PM
It's $K(\mathbb{Z}/p,1)$, and the map comes from taking the homotopy fibre of the fibre sequence
$K(\mathbb{Z},2) \rightarrow K(\mathbb{Z},2) \rightarrow K(\mathbb{Z}/p,2)$ obtained from the corresponding short exact sequence of abelian groups :)
 
Peter Nelson
Peter Nelson
ftr this sequence $BC_p \to BS^1 \to BS^1$ is basically always how people compute various homologies of BC_p
 

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