Quillen plus construction (Ex)
From Manifold Atlas
(Difference between revisions)
| (5 intermediate revisions by one user not shown) | |||
| Line 1: | Line 1: | ||
<wikitex>; | <wikitex>; | ||
| − | Let $X$ be a connected CW-complex. Let $H = [H,H] \ | + | 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 |
| + | |||
| + | * $H_*f$ is an isomorphism. | ||
| + | * $\pi_1(f) : \pi_1X \to \pi_1X_+ = (\pi_1 X)/H$. | ||
| + | |||
| + | In fact, this is unique up to homotopy. | ||
| + | |||
</wikitex> | </wikitex> | ||
[[Category:Exercises]] | [[Category:Exercises]] | ||
[[Category:Exercises without solution]] | [[Category:Exercises without solution]] | ||
Latest revision as of 05:44, 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.
-
.
In fact, this is unique up to homotopy.
