AI 中文总结
该研究探讨三维流形界定四维流形的稳定奇异填充问题，证明闭定向三维流形及部分非定向三维流形存在此类填充，而含双侧$\text{RP}^2$的三维流形不存在。
AI 中文摘要
我们研究哪些三维流形可以以同胚但非稳定微分同胚的方式界定四维流形，稳定化指与若干个$S^2\times S^2$作连通和。我们证明每个闭定向三维流形都存在此类填充，部分非定向三维流形族也存在；与之相对，对于含双侧$\boldsymbol{\text{RP}}^2$的三维流形，任意两个光滑同胚填充都是稳定微分同胚的。
英文摘要
We investigate which 3-manifolds bound 4-manifolds that are homeomorphic but not stably diffeomorphic, where stabilising means taking connected sum with copies of $S^2\times S^2$. We show that every closed, orientable 3-manifold admits such fillings, as do certain families of nonorientable 3-manifolds. In contrast we show that for a 3-manifold containing a 2-sided $\mathbb{RP}^2$, any two smooth, homeomorphic fillings are stably diffeomorphic.
Comments17 pages
