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Topology question

by pivoxa15
Tags: topology
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pivoxa15
#1
Nov4-07, 03:25 AM
P: 2,267
1. The problem statement, all variables and given/known data
What is the torus excluding a disc homeomorphic to?

What is the boundary of a torus (excluding a disc)?


3. The attempt at a solution
RP^2 X RP^2?

As a guess.
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HallsofIvy
#2
Nov4-07, 05:39 AM
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Thanks
PF Gold
P: 39,491
Excluding a disk? You mean you slice a disk out of the torus? What's left is simply connected and looks to me like it is homeomorhic to a ball.
pivoxa15
#3
Nov4-07, 03:15 PM
P: 2,267
Yes, slice out a disk. A torus is a surface so it hollow? A ball is a solid. The torus still has a hole in it. How can it be homeomorphic to a ball?

I'd say it is homeomorphic to a proper torous which is homeomorphic to what?

pivoxa15
#4
Nov4-07, 04:50 PM
P: 2,267
Topology question

What is the boundary of a torus excluding a disc?
matt grime
#5
Nov4-07, 05:52 PM
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P: 9,396
What is it homeorphic to? Infinitely many things, obviously. But I don't immediately see them as being interesting. Now, what is it homotopic to, there is an interesting question.

The boundary of a torus excluding a (closed) disc is obvious, surely. What do you think happens to an object without a boundary if we remove something like a disc?


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