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Some questions about geodesics on surfaces.Geometry/Topology
|Speaker: ||Max Neumann-Coto, UNAM|
|Location: ||2112 MSB|
|Start time: ||Tue, Oct 29 2013, 4:10PM|
For each Riemannian metric on a surface S, one can consider the shortest
geodesics in each homotopy class of curves in S, and how these geodesics
change when the surface is deformed by changing the Riemannian metric.
I will review some known results and present new ones (in collaboration with
Peter Scott) that include bounds for the number of different configurations in
each homotopy class, and for hyperbolic metrics, bounds for the angles of
intersection that depend only on the lengths of the geodesics.
I will also consider the problem of characterizing all the possible "length
functions" (that give the lengths of the shortest geodesics in each homotopy
class) for all metrics on S, and how they relate to the the geometric
intersection numbers between all homotopy classes of curves in S.