Why is the universal cover of RP2 wedge RP2 not S2 wedge S2? [closed]
$begingroup$
I know the universal cover is an infinite wedge of spheres because otherwise there is a problema with the union point but i can't see why right now, could somebody explain that?
algebraic-topology
asked Jan 6 at 9:16
user606273user606273
223
$endgroup$
closed as off-topic by Namaste, Xander Henderson, Eevee Trainer, mrtaurho, max_zorn Jan 14 at 7:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Namaste, Xander Henderson, Eevee Trainer, mrtaurho, max_zorn
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
I know the universal cover is an infinite wedge of spheres because otherwise there is a problema with the union point but i can't see why right now, could somebody explain that?
algebraic-topology
asked Jan 6 at 9:16
user606273user606273
223
$endgroup$
closed as off-topic by Namaste, Xander Henderson, Eevee Trainer, mrtaurho, max_zorn Jan 14 at 7:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Namaste, Xander Henderson, Eevee Trainer, mrtaurho, max_zorn
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
I know the universal cover is an infinite wedge of spheres because otherwise there is a problema with the union point but i can't see why right now, could somebody explain that?
algebraic-topology
asked Jan 6 at 9:16
user606273user606273
223
$endgroup$
I know the universal cover is an infinite wedge of spheres because otherwise there is a problema with the union point but i can't see why right now, could somebody explain that?
algebraic-topology
algebraic-topology
asked Jan 6 at 9:16
user606273user606273
223
asked Jan 6 at 9:16
user606273user606273
223
asked Jan 6 at 9:16
user606273user606273
223
asked Jan 6 at 9:16
user606273user606273
223
asked Jan 6 at 9:16
user606273user606273
223
223
closed as off-topic by Namaste, Xander Henderson, Eevee Trainer, mrtaurho, max_zorn Jan 14 at 7:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Namaste, Xander Henderson, Eevee Trainer, mrtaurho, max_zorn
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Namaste, Xander Henderson, Eevee Trainer, mrtaurho, max_zorn Jan 14 at 7:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Namaste, Xander Henderson, Eevee Trainer, mrtaurho, max_zorn
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Consider any point in $mathbb{R}mathbb{P}^2 veemathbb{R}mathbb{P}^2$ but the union point: it has exactly two pre-images in $S^2 vee S^2$.
On the other hand, the union point has exactly three pre-images in $S^2 vee S^2$.
Therefore, $S^2 vee S^2 rightarrow mathbb{R}mathbb{P}^2 vee mathbb{R}mathbb{P}^2$ is not a covering map.
answered Jan 6 at 9:28
MindlackMindlack
4,900211
$endgroup$
$begingroup$
These all look like smashes.
$endgroup$
– Randall
Jan 6 at 12:05
$begingroup$
Thanks, I had mixed my Latex up...
$endgroup$
– Mindlack
Jan 6 at 12:58
$begingroup$
Yeah that had always bothered me too. I can never remember which way it goes.
$endgroup$
– Randall
Jan 6 at 13:57
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Consider any point in $mathbb{R}mathbb{P}^2 veemathbb{R}mathbb{P}^2$ but the union point: it has exactly two pre-images in $S^2 vee S^2$.
On the other hand, the union point has exactly three pre-images in $S^2 vee S^2$.
Therefore, $S^2 vee S^2 rightarrow mathbb{R}mathbb{P}^2 vee mathbb{R}mathbb{P}^2$ is not a covering map.
answered Jan 6 at 9:28
MindlackMindlack
4,900211
$endgroup$
$begingroup$
These all look like smashes.
$endgroup$
– Randall
Jan 6 at 12:05
$begingroup$
Thanks, I had mixed my Latex up...
$endgroup$
– Mindlack
Jan 6 at 12:58
$begingroup$
Yeah that had always bothered me too. I can never remember which way it goes.
$endgroup$
– Randall
Jan 6 at 13:57
add a comment |
$begingroup$
Consider any point in $mathbb{R}mathbb{P}^2 veemathbb{R}mathbb{P}^2$ but the union point: it has exactly two pre-images in $S^2 vee S^2$.
On the other hand, the union point has exactly three pre-images in $S^2 vee S^2$.
Therefore, $S^2 vee S^2 rightarrow mathbb{R}mathbb{P}^2 vee mathbb{R}mathbb{P}^2$ is not a covering map.
answered Jan 6 at 9:28
MindlackMindlack
4,900211
$endgroup$
$begingroup$
These all look like smashes.
$endgroup$
– Randall
Jan 6 at 12:05
$begingroup$
Thanks, I had mixed my Latex up...
$endgroup$
– Mindlack
Jan 6 at 12:58
$begingroup$
Yeah that had always bothered me too. I can never remember which way it goes.
$endgroup$
– Randall
Jan 6 at 13:57
add a comment |
$begingroup$
Consider any point in $mathbb{R}mathbb{P}^2 veemathbb{R}mathbb{P}^2$ but the union point: it has exactly two pre-images in $S^2 vee S^2$.
On the other hand, the union point has exactly three pre-images in $S^2 vee S^2$.
Therefore, $S^2 vee S^2 rightarrow mathbb{R}mathbb{P}^2 vee mathbb{R}mathbb{P}^2$ is not a covering map.
answered Jan 6 at 9:28
MindlackMindlack
4,900211
$endgroup$
Consider any point in $mathbb{R}mathbb{P}^2 veemathbb{R}mathbb{P}^2$ but the union point: it has exactly two pre-images in $S^2 vee S^2$.
On the other hand, the union point has exactly three pre-images in $S^2 vee S^2$.
Therefore, $S^2 vee S^2 rightarrow mathbb{R}mathbb{P}^2 vee mathbb{R}mathbb{P}^2$ is not a covering map.
answered Jan 6 at 9:28
MindlackMindlack
4,900211
edited Jan 6 at 14:31
answered Jan 6 at 9:28
MindlackMindlack
4,900211
answered Jan 6 at 9:28
MindlackMindlack
4,900211
answered Jan 6 at 9:28
MindlackMindlack
4,900211
4,900211
$begingroup$
These all look like smashes.
$endgroup$
– Randall
Jan 6 at 12:05
$begingroup$
Thanks, I had mixed my Latex up...
$endgroup$
– Mindlack
Jan 6 at 12:58
$begingroup$
Yeah that had always bothered me too. I can never remember which way it goes.
$endgroup$
– Randall
Jan 6 at 13:57
add a comment |
$begingroup$
These all look like smashes.
$endgroup$
– Randall
Jan 6 at 12:05
$begingroup$
Thanks, I had mixed my Latex up...
$endgroup$
– Mindlack
Jan 6 at 12:58
$begingroup$
Yeah that had always bothered me too. I can never remember which way it goes.
$endgroup$
– Randall
Jan 6 at 13:57
$begingroup$
These all look like smashes.
$endgroup$
– Randall
Jan 6 at 12:05
$begingroup$
These all look like smashes.
$endgroup$
– Randall
Jan 6 at 12:05
$begingroup$
Thanks, I had mixed my Latex up...
$endgroup$
– Mindlack
Jan 6 at 12:58
$begingroup$
Thanks, I had mixed my Latex up...
$endgroup$
– Mindlack
Jan 6 at 12:58
$begingroup$
Yeah that had always bothered me too. I can never remember which way it goes.
$endgroup$
– Randall
Jan 6 at 13:57
$begingroup$
Yeah that had always bothered me too. I can never remember which way it goes.
$endgroup$
– Randall
Jan 6 at 13:57
add a comment |
