Aaaaaand the only reason I was able to come up with an "example" so fast is that I completely missed the requirement that the curve be "simple", that is, non-self-crossing. So never mind. On Fri, Oct 22, 2010 at 11:09 PM, Tom Karzes <karzes@sonic.net> wrote:
Hi Jim,
This might be the painting you mentioned:
http://math.berkeley.edu/publications/newsletter/2002/specialinterest.html
A larger, black-and-white photo is available at the bottom of this PDF file:
The article says it was painted in the fall of 1971 by Dennis Sullivan and Bill Thurston.
Tom
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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