Ricci flow and contractibility of spaces of metrics
Ricci flow and contractibility of spaces of metrics
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Bruce Kleiner, New York University
In the lecture I will discuss recent joint work with Richard 听Bamler, which uses Ricci flow through singularities to construct deformations of spaces of metrics on 3-manifolds. 听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. 听We also show that for any spherical space form M, the space of metrics with constant sectional curvature is contractible. 听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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