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arXiv · 2605.04476

Topology of gradient Ricci shrinkers via weighted $L^2$ cohomology

Fei He
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Abstract

This paper proves several topological results for smooth gradient Ricci shrinkers. We establish upper bounds for the Betti numbers, a vanishing theorem for cohomology, and a dichotomy for the number of ends. We also prove a full Hodge theorem for a large class of shrinkers. The methods are based on weighted $L^2$ cohomology and extend to self-shrinkers of the mean curvature flow.

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Fei He. 2026-05-06. Topology of gradient Ricci shrinkers via weighted $L^2$ cohomology. https://arxiv.org/abs/2605.04476

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