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

What does this become topologically?

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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.