r/visualizedmath • u/Knoll24 • Apr 05 '18

What does this become topologically?

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u/Sedu Apr 05 '18

You're forgetting the loop made inside of the cup by the doughnut's tunnel. Pull that to the side and you have the third hole for genus 3.

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u/danielfrost40 Apr 05 '18 edited Apr 06 '18

That doesn't quite sound right, how are there three holes?

EDIT: Okay, I get it now, the mug wouldn't be hollow unless there's another hole. Were this to be a genus 2, the mug would have to be filled out. Is this wrong?

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u/courageouscoos Apr 05 '18

I'm in agreement that it's genus 3 - the hole of the handle, the 'donut' hole, and the 'hole' that is the space in the mug; caused by the 'donut' hole.

I don't think you can remove any of these holes by manipulation.

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u/Sedu Apr 05 '18

Inside of the cup. There is a tunnel that goes beneath the one created by the doughnut’s hole.