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arXiv · 2607.25015

Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature

Jiangcheng You·Heng Zhang
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Abstract

We prove that a contractible $3$-manifold admitting a complete Riemannian metric of nonnegative scalar curvature is diffeomorphic to $\R^3$. We also prove that, if the interior $M_\gamma$ of a compact handlebody of genus $\gamma$ admits such a metric, then $\gamma\leq1$. This answers two open questions posed by Wang and Gromov, respectively.

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Jiangcheng You, Heng Zhang. 2026-07-27. Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature. https://arxiv.org/abs/2607.25015

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