We connect topological changes that can occur in $3$-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena, including relationships between quantum entanglement and wormhole formation. By considering the initial manifold as the $3$-dimensional spatial section of spacetime, we describe the changes of topology occurring in these processes by determining the resulting $3$-manifold and its fundamental group. As these global changes are induced by local processes, we use the local form of Morse functions to provide an algebraic formulation of their temporal evolution and propose a potential energy function which, in some cases, could give rise to the local forces related to surgery. We further show how this topological perspective gives new insight for natural phenomena exhibiting surgery, in all dimensions, while emphasizing the $3$-dimensional case, which describes cosmic phenomena. This work makes new bridges between topology and natural sciences and creates a platform for exploring geometrical physics.

中文翻译：

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宇宙现象中的拓扑手术

我们将通过手术在 3 美元空间中可能发生的拓扑变化与黑洞的形成、虫洞的形成和这些现象的新概括联系起来，包括量子纠缠和虫洞形成之间的关系。通过将初始流形视为时空的 $3$-维空间部分，我们通过确定生成的 $3$-流形及其基本群来描述这些过程中发生的拓扑变化。由于这些全局变化是由局部过程引起的，我们使用莫尔斯函数的局部形式来提供它们的时间演变的代数公式，并提出一个势能函数，在某些情况下，可能会产生与手术相关的局部力。我们进一步展示了这种拓扑视角如何为展示手术的自然现象提供新的见解，在所有维度中，同时强调 $3$ 维度的情况，它描述了宇宙现象。这项工作在拓扑学和自然科学之间架起了新的桥梁，并为探索几何物理学创造了一个平台。