# Topological surgery in cosmic phenomena

## TL;DR

This paper explores how topological surgery in 3-space relates to cosmic phenomena like black holes and wormholes, providing a new mathematical framework linking topology, quantum entanglement, and physical processes.

## Contribution

It introduces a topological approach to modeling cosmic phenomena, connecting local processes with global topological changes using Morse functions and algebraic formulations.

## Key findings

- Topological changes correspond to black hole and wormhole formation.
- A potential energy function models forces related to topological surgery.
- Provides a new perspective linking topology with natural cosmic phenomena.

## Abstract

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.