What is the name of $C(A)/A$
$begingroup$
Given a topological space $A$, $C(A)$ is the cone of $A$. The space $C(A)/A$ is clearly homotopic to the suspension. My question is if it has a widely known name?
general-topology algebraic-topology
edited Nov 8 '13 at 23:27
Stefan Hamcke
21.8k42880
asked Nov 8 '13 at 23:23
Ma MingMa Ming
6,5661331
$endgroup$
add a comment |
$begingroup$
Given a topological space $A$, $C(A)$ is the cone of $A$. The space $C(A)/A$ is clearly homotopic to the suspension. My question is if it has a widely known name?
general-topology algebraic-topology
edited Nov 8 '13 at 23:27
Stefan Hamcke
21.8k42880
asked Nov 8 '13 at 23:23
Ma MingMa Ming
6,5661331
$endgroup$
1
$begingroup$
Isn't this homeomorphic to the suspension? I assume you mean $C(A)/(Atimes{0})$.
$endgroup$
– Stefan Hamcke
Nov 8 '13 at 23:24
$begingroup$
double cone or suspension (don't confuse it with the reduced suspension $A wedge mathbb{S}^1$).
$endgroup$
– user40276
Nov 8 '13 at 23:32
$begingroup$
@StefanH I asked a stupid question. What in my mind is asking the name for the simplicial set $Delta^0 star Acup_{A} Delta^0$ the pushout for the canonical maps $Asubset Delta^0 star A$ and $Ato Delta^0$ for a simplicial set $A$, where star is the simplicial join (a cone).
$endgroup$
– Ma Ming
Nov 9 '13 at 0:33
add a comment |
$begingroup$
Given a topological space $A$, $C(A)$ is the cone of $A$. The space $C(A)/A$ is clearly homotopic to the suspension. My question is if it has a widely known name?
general-topology algebraic-topology
edited Nov 8 '13 at 23:27
Stefan Hamcke
21.8k42880
asked Nov 8 '13 at 23:23
Ma MingMa Ming
6,5661331
$endgroup$
Given a topological space $A$, $C(A)$ is the cone of $A$. The space $C(A)/A$ is clearly homotopic to the suspension. My question is if it has a widely known name?
general-topology algebraic-topology
general-topology algebraic-topology
edited Nov 8 '13 at 23:27
Stefan Hamcke
21.8k42880
asked Nov 8 '13 at 23:23
Ma MingMa Ming
6,5661331
edited Nov 8 '13 at 23:27
Stefan Hamcke
21.8k42880
asked Nov 8 '13 at 23:23
Ma MingMa Ming
6,5661331
edited Nov 8 '13 at 23:27
Stefan Hamcke
21.8k42880
edited Nov 8 '13 at 23:27
Stefan Hamcke
21.8k42880
edited Nov 8 '13 at 23:27
Stefan Hamcke
21.8k42880
21.8k42880
asked Nov 8 '13 at 23:23
Ma MingMa Ming
6,5661331
asked Nov 8 '13 at 23:23
Ma MingMa Ming
6,5661331
asked Nov 8 '13 at 23:23
Ma MingMa Ming
6,5661331
6,5661331
1
$begingroup$
Isn't this homeomorphic to the suspension? I assume you mean $C(A)/(Atimes{0})$.
$endgroup$
– Stefan Hamcke
Nov 8 '13 at 23:24
$begingroup$
double cone or suspension (don't confuse it with the reduced suspension $A wedge mathbb{S}^1$).
$endgroup$
– user40276
Nov 8 '13 at 23:32
$begingroup$
@StefanH I asked a stupid question. What in my mind is asking the name for the simplicial set $Delta^0 star Acup_{A} Delta^0$ the pushout for the canonical maps $Asubset Delta^0 star A$ and $Ato Delta^0$ for a simplicial set $A$, where star is the simplicial join (a cone).
$endgroup$
– Ma Ming
Nov 9 '13 at 0:33
add a comment |
1
$begingroup$
Isn't this homeomorphic to the suspension? I assume you mean $C(A)/(Atimes{0})$.
$endgroup$
– Stefan Hamcke
Nov 8 '13 at 23:24
$begingroup$
double cone or suspension (don't confuse it with the reduced suspension $A wedge mathbb{S}^1$).
$endgroup$
– user40276
Nov 8 '13 at 23:32
$begingroup$
@StefanH I asked a stupid question. What in my mind is asking the name for the simplicial set $Delta^0 star Acup_{A} Delta^0$ the pushout for the canonical maps $Asubset Delta^0 star A$ and $Ato Delta^0$ for a simplicial set $A$, where star is the simplicial join (a cone).
$endgroup$
– Ma Ming
Nov 9 '13 at 0:33
1
1
$begingroup$
Isn't this homeomorphic to the suspension? I assume you mean $C(A)/(Atimes{0})$.
$endgroup$
– Stefan Hamcke
Nov 8 '13 at 23:24
$begingroup$
Isn't this homeomorphic to the suspension? I assume you mean $C(A)/(Atimes{0})$.
$endgroup$
– Stefan Hamcke
Nov 8 '13 at 23:24
$begingroup$
double cone or suspension (don't confuse it with the reduced suspension $A wedge mathbb{S}^1$).
$endgroup$
– user40276
Nov 8 '13 at 23:32
$begingroup$
double cone or suspension (don't confuse it with the reduced suspension $A wedge mathbb{S}^1$).
$endgroup$
– user40276
Nov 8 '13 at 23:32
$begingroup$
@StefanH I asked a stupid question. What in my mind is asking the name for the simplicial set $Delta^0 star Acup_{A} Delta^0$ the pushout for the canonical maps $Asubset Delta^0 star A$ and $Ato Delta^0$ for a simplicial set $A$, where star is the simplicial join (a cone).
$endgroup$
– Ma Ming
Nov 9 '13 at 0:33
$begingroup$
@StefanH I asked a stupid question. What in my mind is asking the name for the simplicial set $Delta^0 star Acup_{A} Delta^0$ the pushout for the canonical maps $Asubset Delta^0 star A$ and $Ato Delta^0$ for a simplicial set $A$, where star is the simplicial join (a cone).
$endgroup$
– Ma Ming
Nov 9 '13 at 0:33
add a comment |
1 Answer
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$begingroup$
This community wiki solution is intended to clear the question from the unanswered queue.
Taken from the comments:
$C(A)/A$ is homeomorphic to the suspension of $A$. Therefore it does not need a separate name.
$endgroup$
add a comment |
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$begingroup$
This community wiki solution is intended to clear the question from the unanswered queue.
Taken from the comments:
$C(A)/A$ is homeomorphic to the suspension of $A$. Therefore it does not need a separate name.
$endgroup$
add a comment |
$begingroup$
This community wiki solution is intended to clear the question from the unanswered queue.
Taken from the comments:
$C(A)/A$ is homeomorphic to the suspension of $A$. Therefore it does not need a separate name.
$endgroup$
add a comment |
$begingroup$
This community wiki solution is intended to clear the question from the unanswered queue.
Taken from the comments:
$C(A)/A$ is homeomorphic to the suspension of $A$. Therefore it does not need a separate name.
$endgroup$
This community wiki solution is intended to clear the question from the unanswered queue.
Taken from the comments:
$C(A)/A$ is homeomorphic to the suspension of $A$. Therefore it does not need a separate name.
answered Dec 29 '18 at 16:27
community wiki
Paul Frost
add a comment |
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$begingroup$
Isn't this homeomorphic to the suspension? I assume you mean $C(A)/(Atimes{0})$.
$endgroup$
– Stefan Hamcke
Nov 8 '13 at 23:24
$begingroup$
double cone or suspension (don't confuse it with the reduced suspension $A wedge mathbb{S}^1$).
$endgroup$
– user40276
Nov 8 '13 at 23:32
$begingroup$
@StefanH I asked a stupid question. What in my mind is asking the name for the simplicial set $Delta^0 star Acup_{A} Delta^0$ the pushout for the canonical maps $Asubset Delta^0 star A$ and $Ato Delta^0$ for a simplicial set $A$, where star is the simplicial join (a cone).
$endgroup$
– Ma Ming
Nov 9 '13 at 0:33