PreprintCC BY 4.0arXiv
Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature
Abstract
We prove that a contractible $3$-manifold admitting a complete Riemannian metric of nonnegative scalar curvature is diffeomorphic to R3. We also prove that, if the interior of a compact handlebody of genus γ admits such a metric, then γ≤1. This answers two open questions posed by Wang and Gromov, respectively.
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BibTeX
@misc{you2026topological,
title = {{Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature}},
author = {Jiangcheng You and Heng Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.25015},
eprint = {2607.25015},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.25015},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature
AU - Jiangcheng You
AU - Heng Zhang
PY - 2026
DA - 2026/11/06
PB - arXiv
DO - 10.48550/arxiv.2607.25015
UR - https://arxiv.org/abs/2607.25015
AB - 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 of a compact handlebody of genus γ admits such a metric, then γ≤1. This answers two open questions posed by Wang and Gromov, respectively.
ER -