Timeline for the space of noncrossing partitions of S^1

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Sep 20, 2013 at 9:48	comment	added	HJRW		Unless I misunderstood your construction, then for each $n\geq2$, your 'space' of partitions is precisely two copies of $S^1$. Each $X_i$ looks like a half-open interval $[a_i,a_{i+1})$ or $(a_i,a_{i+1}]$ that covers precisely $1/n$ of $S^1$, so the whole partition is determined by $a_1$ and the choice of whether to use the first or second sort of half-open interval. As you haven't explained what topology you want to use, I don't know how you want to piece this together as $n\to\infty$. But, thinking of this as a collection of coverings of the circle, perhaps the limiting object is a solenoid?
Sep 20, 2013 at 5:49	answer	added	Christian Stump		timeline score: 2
Sep 20, 2013 at 4:16	comment	added	HJRW		What topology are you putting on it?
Sep 19, 2013 at 23:55	history	asked	john mangual	CC BY-SA 3.0