简单连通四维流形的正标量曲率与异构结构
微分几何
2025-01-28 v2 几何拓扑
摘要
我们讨论了Gromov的带宽不等式和Rosenberg关于稳定性猜想在简单连通光滑四维流形上的情况。由于基于Seiberg-Witten不变量的反例，这两个结果在四维空间已知为假。然而，我们证明了在考虑简单连通光滑四维流形至同胚的情况下，这两个结果仍然成立。我们也获得了关于非简单连通光滑四维流形的相关结果。
引用
@article{arxiv.2501.01113,
title = {Positive scalar curvature and exotic structures on simply connected four manifolds},
author = {Aditya Kumar and Balarka Sen},
journal= {arXiv preprint arXiv:2501.01113},
year = {2025}
}
备注
v2. 19 pages. Substantially revised: Corrected lemmas and significantly simplified proofs in Section 3, added a new result for non-simply connected 4-manifolds. Minor improvements in exposition