Finding linking numbers when 1 handles are in the diagram

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In the diagram above, what is the linking number of the red with the green? If the blue 2-handle were absent, I could see just sliding the "dumbells" past eachother and their linking would be zero.



Also, does anyone have any idea which 2-handle slides (and subsequent 1/2-handle cancellations) will turn this into a 0-framed right handed trefoil? (Gompf & Stipsicz ex. 5.1.8(b))




low-dimensional-topology




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  • What happend if you push one of the sphere via the red curve towards the other sphere? Same as green then?
    – Anubhav Mukherjee
    Jul 20 at 18:23














up vote
0
down vote

favorite












enter image description here



In the diagram above, what is the linking number of the red with the green? If the blue 2-handle were absent, I could see just sliding the "dumbells" past eachother and their linking would be zero.



Also, does anyone have any idea which 2-handle slides (and subsequent 1/2-handle cancellations) will turn this into a 0-framed right handed trefoil? (Gompf & Stipsicz ex. 5.1.8(b))




low-dimensional-topology




share|cite|improve this question



















  • What happend if you push one of the sphere via the red curve towards the other sphere? Same as green then?
    – Anubhav Mukherjee
    Jul 20 at 18:23












up vote
0
down vote

favorite









up vote
0
down vote

favorite











enter image description here



In the diagram above, what is the linking number of the red with the green? If the blue 2-handle were absent, I could see just sliding the "dumbells" past eachother and their linking would be zero.



Also, does anyone have any idea which 2-handle slides (and subsequent 1/2-handle cancellations) will turn this into a 0-framed right handed trefoil? (Gompf & Stipsicz ex. 5.1.8(b))




low-dimensional-topology




share|cite|improve this question











enter image description here



In the diagram above, what is the linking number of the red with the green? If the blue 2-handle were absent, I could see just sliding the "dumbells" past eachother and their linking would be zero.



Also, does anyone have any idea which 2-handle slides (and subsequent 1/2-handle cancellations) will turn this into a 0-framed right handed trefoil? (Gompf & Stipsicz ex. 5.1.8(b))





low-dimensional-topology





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 20 at 16:59









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  • What happend if you push one of the sphere via the red curve towards the other sphere? Same as green then?
    – Anubhav Mukherjee
    Jul 20 at 18:23
















  • What happend if you push one of the sphere via the red curve towards the other sphere? Same as green then?
    – Anubhav Mukherjee
    Jul 20 at 18:23















What happend if you push one of the sphere via the red curve towards the other sphere? Same as green then?
– Anubhav Mukherjee
Jul 20 at 18:23




What happend if you push one of the sphere via the red curve towards the other sphere? Same as green then?
– Anubhav Mukherjee
Jul 20 at 18:23















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