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Manifold Convergence: Sewing Sequences Of Riemannian Manifolds With Positive Or Nonnegative Scalar Curvature, Jorge E. Basilio
Manifold Convergence: Sewing Sequences Of Riemannian Manifolds With Positive Or Nonnegative Scalar Curvature, Jorge E. Basilio
Dissertations, Theses, and Capstone Projects
In this thesis, we develop a new method of performing surgery on 3-dimensional manifolds called "sewing" and use this technique to construct sequences of Riemannian manifolds with positive or nonnegative scalar curvature. The foundation of our method is a strengthening of the Gromov-Lawson tunnel construction which guarantees the existence of “tiny” and arbitrarily “short” tunnels. We study the limits of sequences of sewn spaces under the Gromov-Hausdorff (GH) and Sormani-Wenger Instrinsic-Flat (SWIF) distances and discuss to what extent the notion of scalar curvature extends to these spaces. We give three applications of the sewing technique to demonstrate that stability theorems …