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Joint Princeton-Rutgers Seminar on Geometric PDE's

Ricci flow and contractibility of spaces of metrics 

Bruce Kleiner, Courant Institute

Location:  Fine Hall 314, Princeton University
Date & time: Wednesday, 16 October 2019 at 3:00PM - 4:00PM

Abstract: In the lecture I will discuss recent joint work with Richard Bamler, which uses Ricci flow through singularities to construct deformations of spaces of metrics on 3-manifolds. We show that the space of metrics with positive scalar on any 3-manifold is either contractible or empty; this extends earlier work by Fernando Marques, which proved path-connectedness. We also show that for any spherical space form M, the space of metrics with constant sectional curvature is contractible. This completes the proof of the Generalized Smale Conjecture, and gives a new proof of the original Smale Conjecture for S^3. 

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