Topology question

  1. 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.
     
    Last edited: Nov 4, 2007
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,509
    Staff Emeritus
    Science Advisor

    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.
     
  4. 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?
     
    Last edited: Nov 4, 2007
  5. What is the boundary of a torus excluding a disc?
     
  6. matt grime

    matt grime 9,396
    Science Advisor
    Homework Helper

    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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