Topology of tame contractible n-manifolds, n=6,7, with Positive BiRicci Curvature and Ricci lower bounds
Abstract
We show that if an open smooth $6$-manifold M6 is the interior of a compact, contractible manifold with boundary X6, such that π3(X,∂ X)=0, and M supports a complete metric with uniform positive BiRicci curvature and Ricci curvature bounded below, then M is diffeomorphic to ℝ6. Additionally, we show that if an open smooth n-manifold Mn, n∈{6,7}, is the interior of a compact, contractible manifold with boundary Xn, such that π3(X,∂ X)=0, and M supports a complete metric with positive BiRicci curvature with at most C-quadratic decay at infinity for some C>Cn and nonnegative Ricci curvature, then M is diffeomorphic to ℝn. Lastly, for each n≥6, we construct a compact, contractible Newman n-manifold, Nn, based on a presentation of the Higman group such that πi(N,∂ N)=0, 3≤ i ≤ n−3, and int(N) admits a complete metric with uniform positive scalar curvature and Ricci curvature bounded below.
Related
- Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds
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- Positive scalar curvature on products of noncompact manifolds
- Sharp monotonicity for closed three-manifolds with positive scalar curvature
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BibTeX
@misc{jr2026topology,
title = {{Topology of tame contractible $n$-manifolds, $n=6,7$, with Positive BiRicci Curvature and Ricci lower bounds}},
author = {Paul Sweeney Jr},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08686},
eprint = {2610.08686},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08686},
}
RIS
TY - UNPB
TI - Topology of tame contractible n-manifolds, n=6,7, with Positive BiRicci Curvature and Ricci lower bounds
AU - Paul Sweeney Jr
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.08686
UR - https://arxiv.org/abs/2610.08686
AB - We show that if an open smooth $6$-manifold M^6 is the interior of a compact, contractible manifold with boundary X^6, such that π_3(X,∂ X)=0, and M supports a complete metric with uniform positive BiRicci curvature and Ricci curvature bounded below, then M is diffeomorphic to ℝ^6. Additionally, we show that if an open smooth n-manifold M^n, n∈{6,7}, is the interior of a compact, contractible manifold with boundary X^n, such that π_3(X,∂ X)=0, and M supports a complete metric with positive BiRicci curvature with at most C-quadratic decay at infinity for some C>C_n and nonnegative Ricci curvature, then M is diffeomorphic to ℝ^n. Lastly, for each n≥6, we construct a compact, contractible Newman n-manifold, N^n, based on a presentation of the Higman group such that π_i(N,∂ N)=0, 3≤ i ≤ n−3, and int(N) admits a complete metric with uniform positive scalar curvature and Ricci curvature bounded below.
ER -