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.
enter image description here



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







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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















up vote
4
down vote

favorite
2












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.
enter image description here



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







share|cite|improve this question






















  • 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













up vote
4
down vote

favorite
2









up vote
4
down vote

favorite
2






2





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.
enter image description here



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







share|cite|improve this question













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.
enter image description here



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






share|cite|improve this question













share|cite|improve this question











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share|cite|improve this question










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


















  • 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










1 Answer
1






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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.






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    1 Answer
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    1 Answer
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    active

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    up vote
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    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.






    share|cite|improve this answer

























      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.






      share|cite|improve this answer























        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.






        share|cite|improve this answer












        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.







        share|cite|improve this answer












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        answered Nov 17 at 23:08









        CyclotomicField

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