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arXiv · 1911.02152

Sequences of three dimensional manifolds with positive scalar curvature

J. Basilio·C. Sormani
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Abstract

We develop two new methods of constructing sequences of manifolds with positive scalar curvature that converge in the Gromov-Hausdorff and Intrinsic Flat sense to limit spaces with "pulled regions". The examples created rigorously within using these methods were announced by us a few years ago and have influenced the statements of some of Gromov's conjectures concerning sequences of manifolds with positive scalar curvature. Both methods extend the notion of "sewing along a curve" developed in prior work of the authors with Dodziuk to create limits that are pulled string spaces. The first method allows us to sew any compact set in a fixed initial manifold to create a limit space in which that compact set has been scrunched to a single point. The second method allows us to edit a sequence of regions or curves in a sequence of distinct manifolds.

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J. Basilio, C. Sormani. 2019-11-06. Sequences of three dimensional manifolds with positive scalar curvature. https://arxiv.org/abs/1911.02152

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