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From: Mariano Suárez-Alvarez on 19 Jul 2008 15:39
On Jul 19, 2:18 pm, nullgraph <nullgr...(a)gmail.com> wrote:
> On Jul 18, 5:32 pm, Mariano Suárez-Alvarez
>
>
>
> <mariano.suarezalva...(a)gmail.com> wrote:
> > On Jul 18, 6:01 pm, nullgraph <nullgr...(a)gmail.com> wrote:
>
> > > On Jul 18, 4:47 pm, Mariano Suárez-Alvarez
>
> > > <mariano.suarezalva...(a)gmail.com> wrote:
> > > > On Jul 18, 4:39 pm, nullgraph <nullgr...(a)gmail.com> wrote:
>
> > > > > Hi, I'm trying to calculate the fundamental group of the Klein bottle.
> > > > > I know I should be using Van Kampen and start with removing a point
> > > > > from the Klein bottle. I'm thinking of breaking the Klein bottle into
> > > > > 2 parts, one is a circle without the removed point and the other is
> > > > > everything except the removed point. How do I continue from there? I
> > > > > read in a previous thread that the 2nd part (punctured Klein bottle)
> > > > > is homotopic to the figure-eight, why is that?
> > > > > Thank you.
>
> > Please do not top-post.
>
> > Forget about the Klein bottle and the torus.
> > Can you see why a punctured *rectangle* (with no
> > identifications) is homotopic to a circle?
>
> > -- m
>
> I'm confused... where and how did I top-post?
>
> Yes, I can see why a punctured rectangle with no identification is
> homotopic to a circle. I guess the identification is the part that
> confuse me.

And what argument do you use to make sure that the
punctured rectangle is homotopic to its boundary?
Can you use the same argument for the puctured torus
and for the puctured Klein bottle?

-- m
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