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Math Help - Homeomorphism of connected sums

  1. #1
    Member ModusPonens's Avatar
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    Homeomorphism of connected sums

    Hello.

    I'd like to know how to solve the following problem: \mathbb{R}P^2# T^2=\mathbb{R}P^2# K^2 , where \mathbb{R}P^2 is the real projective plane, T^2 is the torus and K^2 is the Klein bottle.

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  2. #2
    Member ModusPonens's Avatar
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    Re: Homeomorphism of connected sums

    I think I did not explain myself well when posting this.

    The problem is to prove the equality. But no equations are necessary. For example, in a previous exercise it's asked to prove that S^2 is the identity in the operation #. It sufices to say that a sphere without a part that is homeomorphic to an open disk D^2 is homeomorphic to a closed disk.

    If that's not the problem, could you tell me if this problem is a hard one for a 3rd year student of mathematics?

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  3. #3
    GJA
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    Re: Homeomorphism of connected sums

    Hi, ModusPonens. I haven't done a problem like this in awhile, but there is essentially a procedure you follow to do stuff like this. It starts with using the polygonal representation for the connected sums and going from there using cuting/pasting techniques. Check out a book by Christine Kinsey for the steps.
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    Re: Homeomorphism of connected sums

    Thanks for your sharing.I will concern about it.








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