Moduli spaces with no nonpositively curved metrics of bounded geometry

Geometry Topology Seminar
Friday, May 18, 2012 - 13:05
1 hour (actually 50 minutes)
Skiles 006
Brown University
We prove the moduli space M_{g,n} of the surface of g genus with n punctures admits no complete, visible, nonpositively curved Riemannian metric, which will give a connection between conjectures from P.Eberlein and Brock-Farb. Motivated from this connection, we will prove that the translation length of a parabolic isometry of a proper visible CAT(0) space is zero. As an application of this zero property, we will give a detailed answer toP.Eberlein's conjecture.