Geometry & Topology

Event Information Convexity of balls in the outer space
16:10 on Monday October 23, 2017
17:00 on Monday October 23, 2017
BA6183, Bahen Center, 40 St. George St.
Yulan Qing

University of Toronto

In this talk we answer questions regarding the convexity properties of geodesics and balls in Outer space equipped with the Lipschitz metric. We introduce a class of geodesics called balanced folding paths and show that, for every loop α, the length of α along a balanced folding path is not larger than the maximum of its lengths at the end points. This implies that out-going balls are weakly convex. We then show that these results are sharp by providing several counterexamples.