I have just drawn one that is so simple it must be the simplest. I guess I could run it over to your house if you want to stay up a few more minutes. I don't know the proof for two holes, but it sounds like a corollary of some fixed-point theorem. On Fri, Oct 22, 2010 at 10:40 PM, James Propp <jpropp@cs.uml.edu> wrote:
What's the simplest example of a simple closed curve in the triply-punctured plane that has winding number 0 around each of the punctures but is not contractible? (Back when I was in grad school in Berkeley in the '80s, there was a painting of one such curve on the wall, along with the associated word in the fundamental group of the surface.) Also, what's the simplest way to prove that no analogous curve exists for the doubly-punctured plane?
Jim Propp
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