What's wrong with my deformation retract?
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I drew a deformation retract of the twice punctured genus 2-torus. It would seem that this should deformation retract to a bouquet of 3 circles.
One the other hand, computing the Euler-characteristics shows that it should deformation retract to a bouquet of 5 circles.
If anyone could explain what I'm doing wrong, I would appreciate it!
algebraic-topology fake-proofs
asked Nov 17 at 22:18
MathUser_NotPrime
1,019112
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up vote
4
down vote
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I drew a deformation retract of the twice punctured genus 2-torus. It would seem that this should deformation retract to a bouquet of 3 circles.
One the other hand, computing the Euler-characteristics shows that it should deformation retract to a bouquet of 5 circles.
If anyone could explain what I'm doing wrong, I would appreciate it!
algebraic-topology fake-proofs
asked Nov 17 at 22:18
MathUser_NotPrime
1,019112
Can the two punctures be deformed into the middle circle? I would think they would deform to be circles tangent to the two horizontal circles on their outsides.
– John Douma
Nov 17 at 23:08
add a comment |
up vote
4
down vote
favorite
up vote
4
down vote
favorite
I drew a deformation retract of the twice punctured genus 2-torus. It would seem that this should deformation retract to a bouquet of 3 circles.
One the other hand, computing the Euler-characteristics shows that it should deformation retract to a bouquet of 5 circles.
If anyone could explain what I'm doing wrong, I would appreciate it!
algebraic-topology fake-proofs
asked Nov 17 at 22:18
MathUser_NotPrime
1,019112
I drew a deformation retract of the twice punctured genus 2-torus. It would seem that this should deformation retract to a bouquet of 3 circles.
One the other hand, computing the Euler-characteristics shows that it should deformation retract to a bouquet of 5 circles.
If anyone could explain what I'm doing wrong, I would appreciate it!
algebraic-topology fake-proofs
algebraic-topology fake-proofs
asked Nov 17 at 22:18
MathUser_NotPrime
1,019112
asked Nov 17 at 22:18
MathUser_NotPrime
1,019112
asked Nov 17 at 22:18
MathUser_NotPrime
1,019112
asked Nov 17 at 22:18
MathUser_NotPrime
1,019112
asked Nov 17 at 22:18
MathUser_NotPrime
1,019112
1,019112
Can the two punctures be deformed into the middle circle? I would think they would deform to be circles tangent to the two horizontal circles on their outsides.
– John Douma
Nov 17 at 23:08
add a comment |
Can the two punctures be deformed into the middle circle? I would think they would deform to be circles tangent to the two horizontal circles on their outsides.
– John Douma
Nov 17 at 23:08
Can the two punctures be deformed into the middle circle? I would think they would deform to be circles tangent to the two horizontal circles on their outsides.
– John Douma
Nov 17 at 23:08
Can the two punctures be deformed into the middle circle? I would think they would deform to be circles tangent to the two horizontal circles on their outsides.
– John Douma
Nov 17 at 23:08
add a comment |
1 Answer
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The shaded areas seem to ignoring the center of each torus as you move the boundary of the puncture points past them and so the third and fourth step are erroneous.
answered Nov 17 at 23:08
CyclotomicField
2,0891312
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
The shaded areas seem to ignoring the center of each torus as you move the boundary of the puncture points past them and so the third and fourth step are erroneous.
answered Nov 17 at 23:08
CyclotomicField
2,0891312
add a comment |
up vote
3
down vote
accepted
The shaded areas seem to ignoring the center of each torus as you move the boundary of the puncture points past them and so the third and fourth step are erroneous.
answered Nov 17 at 23:08
CyclotomicField
2,0891312
add a comment |
up vote
3
down vote
accepted
up vote
3
down vote
accepted
The shaded areas seem to ignoring the center of each torus as you move the boundary of the puncture points past them and so the third and fourth step are erroneous.
answered Nov 17 at 23:08
CyclotomicField
2,0891312
The shaded areas seem to ignoring the center of each torus as you move the boundary of the puncture points past them and so the third and fourth step are erroneous.
answered Nov 17 at 23:08
CyclotomicField
2,0891312
answered Nov 17 at 23:08
CyclotomicField
2,0891312
answered Nov 17 at 23:08
CyclotomicField
2,0891312
answered Nov 17 at 23:08
CyclotomicField
2,0891312
2,0891312
add a comment |
add a comment |
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Can the two punctures be deformed into the middle circle? I would think they would deform to be circles tangent to the two horizontal circles on their outsides.
– John Douma
Nov 17 at 23:08