Quillen plus construction (Ex)
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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 | 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 | ||
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| − | + | * $H_*f$ is an isomorphism. | |
| − | + | * $\pi_1(f) : \pi_1X \to \pi_1X_+ = \pi_1 X/H$. | |
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</wikitex> | </wikitex> | ||
[[Category:Exercises]] | [[Category:Exercises]] | ||
[[Category:Exercises without solution]] | [[Category:Exercises without solution]] | ||
Revision as of 05:41, 8 January 2019
Let 
be a connected CW-complex. Let ![H = [H,H] \triangleleft \pi_1X](/images/math/b/0/d/b0d95d2043e2c874d235445b5b0a17a0.png)
. Show there exists a map 
so that
-
is an isomorphism.
-
.
