Mixing
Homotopy classes of maps into the skeleta of CW complexes
$begingroup$
Suppse $Y$ is a connected CW complex and $Y_n$ denotes the $n$-skeleton of $Y$. Suppose $X$ is a connected CW complex of dimension $n$. The inclusion $iota colon Y_n to Y$ yields a map $[X,Y_n] to [X,Y]$. Is this map surjective?
I was thinking as follows. For a map $Xto Y$ let be $X to Y_n$ a cellular map homotopic to the previous one. Is then this map $X to Y_n$ mapped onto the map $Xto Y$ by
the inclusion $iota$?
algebraic-topology homotopy-theory
asked Jan 23 at 14:59
Wilhelm L.Wilhelm L.
41117
$endgroup$
add a comment |
$begingroup$
Suppse $Y$ is a connected CW complex and $Y_n$ denotes the $n$-skeleton of $Y$. Suppose $X$ is a connected CW complex of dimension $n$. The inclusion $iota colon Y_n to Y$ yields a map $[X,Y_n] to [X,Y]$. Is this map surjective?
I was thinking as follows. For a map $Xto Y$ let be $X to Y_n$ a cellular map homotopic to the previous one. Is then this map $X to Y_n$ mapped onto the map $Xto Y$ by
the inclusion $iota$?
algebraic-topology homotopy-theory
asked Jan 23 at 14:59
Wilhelm L.Wilhelm L.
41117
$endgroup$
1
$begingroup$
Yes (up to homotopy).
$endgroup$
– Aleksandar Milivojevic
Jan 23 at 15:07
$begingroup$
Let me add "by definition" to Aleksandar's answer
$endgroup$
– Max
Jan 23 at 15:46
add a comment |
$begingroup$
Suppse $Y$ is a connected CW complex and $Y_n$ denotes the $n$-skeleton of $Y$. Suppose $X$ is a connected CW complex of dimension $n$. The inclusion $iota colon Y_n to Y$ yields a map $[X,Y_n] to [X,Y]$. Is this map surjective?
I was thinking as follows. For a map $Xto Y$ let be $X to Y_n$ a cellular map homotopic to the previous one. Is then this map $X to Y_n$ mapped onto the map $Xto Y$ by
the inclusion $iota$?
algebraic-topology homotopy-theory
asked Jan 23 at 14:59
Wilhelm L.Wilhelm L.
41117
$endgroup$
Suppse $Y$ is a connected CW complex and $Y_n$ denotes the $n$-skeleton of $Y$. Suppose $X$ is a connected CW complex of dimension $n$. The inclusion $iota colon Y_n to Y$ yields a map $[X,Y_n] to [X,Y]$. Is this map surjective?
I was thinking as follows. For a map $Xto Y$ let be $X to Y_n$ a cellular map homotopic to the previous one. Is then this map $X to Y_n$ mapped onto the map $Xto Y$ by
the inclusion $iota$?
algebraic-topology homotopy-theory
algebraic-topology homotopy-theory
asked Jan 23 at 14:59
Wilhelm L.Wilhelm L.
41117
asked Jan 23 at 14:59
Wilhelm L.Wilhelm L.
41117
asked Jan 23 at 14:59
Wilhelm L.Wilhelm L.
41117
asked Jan 23 at 14:59
Wilhelm L.Wilhelm L.
41117
asked Jan 23 at 14:59
Wilhelm L.Wilhelm L.
41117
41117
1
$begingroup$
Yes (up to homotopy).
$endgroup$
– Aleksandar Milivojevic
Jan 23 at 15:07
$begingroup$
Let me add "by definition" to Aleksandar's answer
$endgroup$
– Max
Jan 23 at 15:46
add a comment |
1
$begingroup$
Yes (up to homotopy).
$endgroup$
– Aleksandar Milivojevic
Jan 23 at 15:07
$begingroup$
Let me add "by definition" to Aleksandar's answer
$endgroup$
– Max
Jan 23 at 15:46
1
1
$begingroup$
Yes (up to homotopy).
$endgroup$
– Aleksandar Milivojevic
Jan 23 at 15:07
$begingroup$
Yes (up to homotopy).
$endgroup$
– Aleksandar Milivojevic
Jan 23 at 15:07
$begingroup$
Let me add "by definition" to Aleksandar's answer
$endgroup$
– Max
Jan 23 at 15:46
$begingroup$
Let me add "by definition" to Aleksandar's answer
$endgroup$
– Max
Jan 23 at 15:46
add a comment |
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$begingroup$
Yes (up to homotopy).
$endgroup$
– Aleksandar Milivojevic
Jan 23 at 15:07
$begingroup$
Let me add "by definition" to Aleksandar's answer
$endgroup$
– Max
Jan 23 at 15:46