Quillen plus construction (Ex)
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− | Let $X$ be a connected CW-complex. Let $H = [H,H] \triangleleft \pi_1X$ | + | Let $X$ be a connected CW-complex. Let $H = [H,H] \triangleleft \pi_1X$. Show there exists a map $f : X \to X_+$ so that |
+ | \begin{itemize} | ||
+ | \item $H_*f$ is an isomorphism. | ||
+ | \item $\pi_1(f) : \pi_1X \to \pi_1X_+ = \pi_1 X/H$. | ||
+ | \end{itemize} | ||
</wikitex> | </wikitex> | ||
[[Category:Exercises]] | [[Category:Exercises]] | ||
[[Category:Exercises without solution]] | [[Category:Exercises without solution]] |
Revision as of 05:40, 8 January 2019
Let be a connected CW-complex. Let . Show there exists a map so that \begin{itemize} \item is an isomorphism. \item . \end{itemize}