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SUMMARY:Curvature\, Sphere Theorems\, and the Ricci Flow - Prof. Simon Bre
 ndle (Stanford)
DTSTART:20121119T170000Z
DTEND:20121119T180000Z
UID:TALK41550@talks.cam.ac.uk
CONTACT:Shepherd-Barron
DESCRIPTION:In 1926\, Hopf proved that any compact\, simply connected Riem
 annian manifold with constant curvature 1 is isometric\nto the standard sp
 here. Motivated by this result\, Hopf posed the question of whether a comp
 act\, simply connected manifold\nwith suitably pinched curvature is topolo
 gically a sphere. This question has been studied by many authors over the 
 past six\ndecades\, a milestone being the Topological Sphere Theorem prove
 d by Berger and Klingenberg in 1960.\n\nIn this lecture\, I will discuss t
 he history of this problem\, and describe the proof (joint with R. Schoen)
  of the\nDifferentiable Sphere Theorem. This theorem classifies all manifo
 lds with 1/4-pinched curvature up to diffeomorphism. The\ndistinction betw
 een homeomorphism and diffeomorphism is significant in light of the exotic
  spheres constructed by Milnor\;\nthe proof uses the Ricci flow technique 
 pioneered by Hamilton.
LOCATION:MR2\, Centre for Mathematical Sciences
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