Constructs closed aspherical 4-manifolds that are homeomorphic but not diffeomorphic, providing counterexamples to the smooth Borel conjecture in dimension 4.
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Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
20 Pith papers cite this work. Polarity classification is still indexing.
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Let M be a closed oriented three-manifold, whose prime decomposition contains no aspherical factors. We show that for any initial riemannian metric on M the solution to the Ricci flow with surgery, defined in our previous paper math.DG/0303109, becomes extinct in finite time. The proof uses a version of the minimal disk argument from 1999 paper by Richard Hamilton, and a regularization of the curve shortening flow, worked out by Altschuler and Grayson.
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A perturbative Ricci-flow formulation in gravity yields a renormalization scheme for Newton's constant that exhibits a non-Gaussian fixed point at two-loop order.
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