fundamental group of torus with segment that connecting two points of it
0
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Let X be the topological space obtained by gluing on torus a segment that connecting two point of torus. Use Seifert Van Kampen's theorem to calculate the fundamental group of X.
I try to compute it but I can't do it.
algebraic-topology
asked Dec 13 '18 at 11:25
Antonio Antonio
61
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|
show 3 more comments
0
$begingroup$
Let X be the topological space obtained by gluing on torus a segment that connecting two point of torus. Use Seifert Van Kampen's theorem to calculate the fundamental group of X.
I try to compute it but I can't do it.
algebraic-topology
asked Dec 13 '18 at 11:25
Antonio Antonio
61
$endgroup$
$begingroup$
Can you explain more precisely how $X$ is constructed? Do you mean that you attach $[0,1]$ to the torus $T$ via an injective map ${ 0,1 } to T$?
$endgroup$
– Paul Frost
Dec 13 '18 at 12:33
$begingroup$
Isn't this the same as the question you asked (and I answered) earlier?
$endgroup$
– Aweygan
Dec 13 '18 at 14:33
$begingroup$
No, it’s another exercise
$endgroup$
– Antonio
Dec 13 '18 at 16:02
$begingroup$
The segment that connetting two points of Torus is attached to the torus. I must compute fundamental group of space formed by torus with this segment
$endgroup$
– Antonio
Dec 13 '18 at 16:08
$begingroup$
In the last question torus was constructed attacching two points, in this question torus is constructed attacching a segment that connetting two points
$endgroup$
– Antonio
Dec 13 '18 at 16:15
|
show 3 more comments
0
0
0
$begingroup$
Let X be the topological space obtained by gluing on torus a segment that connecting two point of torus. Use Seifert Van Kampen's theorem to calculate the fundamental group of X.
I try to compute it but I can't do it.
algebraic-topology
asked Dec 13 '18 at 11:25
Antonio Antonio
61
$endgroup$
Let X be the topological space obtained by gluing on torus a segment that connecting two point of torus. Use Seifert Van Kampen's theorem to calculate the fundamental group of X.
I try to compute it but I can't do it.
algebraic-topology
algebraic-topology
asked Dec 13 '18 at 11:25
Antonio Antonio
61
asked Dec 13 '18 at 11:25
Antonio Antonio
61
asked Dec 13 '18 at 11:25
Antonio Antonio
61
asked Dec 13 '18 at 11:25
Antonio Antonio
61
asked Dec 13 '18 at 11:25
Antonio Antonio
61
61
$begingroup$
Can you explain more precisely how $X$ is constructed? Do you mean that you attach $[0,1]$ to the torus $T$ via an injective map ${ 0,1 } to T$?
$endgroup$
– Paul Frost
Dec 13 '18 at 12:33
$begingroup$
Isn't this the same as the question you asked (and I answered) earlier?
$endgroup$
– Aweygan
Dec 13 '18 at 14:33
$begingroup$
No, it’s another exercise
$endgroup$
– Antonio
Dec 13 '18 at 16:02
$begingroup$
The segment that connetting two points of Torus is attached to the torus. I must compute fundamental group of space formed by torus with this segment
$endgroup$
– Antonio
Dec 13 '18 at 16:08
$begingroup$
In the last question torus was constructed attacching two points, in this question torus is constructed attacching a segment that connetting two points
$endgroup$
– Antonio
Dec 13 '18 at 16:15
|
show 3 more comments
$begingroup$
Can you explain more precisely how $X$ is constructed? Do you mean that you attach $[0,1]$ to the torus $T$ via an injective map ${ 0,1 } to T$?
$endgroup$
– Paul Frost
Dec 13 '18 at 12:33
$begingroup$
Isn't this the same as the question you asked (and I answered) earlier?
$endgroup$
– Aweygan
Dec 13 '18 at 14:33
$begingroup$
No, it’s another exercise
$endgroup$
– Antonio
Dec 13 '18 at 16:02
$begingroup$
The segment that connetting two points of Torus is attached to the torus. I must compute fundamental group of space formed by torus with this segment
$endgroup$
– Antonio
Dec 13 '18 at 16:08
$begingroup$
In the last question torus was constructed attacching two points, in this question torus is constructed attacching a segment that connetting two points
$endgroup$
– Antonio
Dec 13 '18 at 16:15
$begingroup$
Can you explain more precisely how $X$ is constructed? Do you mean that you attach $[0,1]$ to the torus $T$ via an injective map ${ 0,1 } to T$?
$endgroup$
– Paul Frost
Dec 13 '18 at 12:33
$begingroup$
Can you explain more precisely how $X$ is constructed? Do you mean that you attach $[0,1]$ to the torus $T$ via an injective map ${ 0,1 } to T$?
$endgroup$
– Paul Frost
Dec 13 '18 at 12:33
$begingroup$
Isn't this the same as the question you asked (and I answered) earlier?
$endgroup$
– Aweygan
Dec 13 '18 at 14:33
$begingroup$
Isn't this the same as the question you asked (and I answered) earlier?
$endgroup$
– Aweygan
Dec 13 '18 at 14:33
$begingroup$
No, it’s another exercise
$endgroup$
– Antonio
Dec 13 '18 at 16:02
$begingroup$
No, it’s another exercise
$endgroup$
– Antonio
Dec 13 '18 at 16:02
$begingroup$
The segment that connetting two points of Torus is attached to the torus. I must compute fundamental group of space formed by torus with this segment
$endgroup$
– Antonio
Dec 13 '18 at 16:08
$begingroup$
The segment that connetting two points of Torus is attached to the torus. I must compute fundamental group of space formed by torus with this segment
$endgroup$
– Antonio
Dec 13 '18 at 16:08
$begingroup$
In the last question torus was constructed attacching two points, in this question torus is constructed attacching a segment that connetting two points
$endgroup$
– Antonio
Dec 13 '18 at 16:15
$begingroup$
In the last question torus was constructed attacching two points, in this question torus is constructed attacching a segment that connetting two points
$endgroup$
– Antonio
Dec 13 '18 at 16:15
|
show 3 more comments
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$begingroup$
Can you explain more precisely how $X$ is constructed? Do you mean that you attach $[0,1]$ to the torus $T$ via an injective map ${ 0,1 } to T$?
$endgroup$
– Paul Frost
Dec 13 '18 at 12:33
$begingroup$
Isn't this the same as the question you asked (and I answered) earlier?
$endgroup$
– Aweygan
Dec 13 '18 at 14:33
$begingroup$
No, it’s another exercise
$endgroup$
– Antonio
Dec 13 '18 at 16:02
$begingroup$
The segment that connetting two points of Torus is attached to the torus. I must compute fundamental group of space formed by torus with this segment
$endgroup$
– Antonio
Dec 13 '18 at 16:08
$begingroup$
In the last question torus was constructed attacching two points, in this question torus is constructed attacching a segment that connetting two points
$endgroup$
– Antonio
Dec 13 '18 at 16:15