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4:00 pm Wednesday, September 5, 2012 Geometry-Analysis Seminar: Iteration of mapping classes and limits of Weil-Petersson geodesics by Yunhui Wu (Rice University) in HB 227- Abstract: Let $S=S_{g,n}$ be a surface of negative Euler-characteristic, of genus $g$, and with $n$ punctures. Let $Teich(S)$ be the Teichm\"uller space endowed with the Weil-Petersson metric and $Mod(S)$ be the mapping class group of $S$. Fix $X,Y\in Teich(S)$. In this paper, we show that for any $\phi \in Mod(S)$, there exists a positive integer $k$ depending on $\phi$ such that the sequence of the directions of geodesics connecting $X$ and $\phi^{kn}\circ{Y}$ is convergent in the visual sphere of $X$. Moreover we will give a geometric description for the geodesic whose direction is the limit.
Submitted by mwolf@rice.edu |