The Realization of 3D Topological Spaces Branched over Graphs
Abstract
In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in dimension 3, and a complete set of the fundamental groups realized over several graphs is found. We also include some new visualizations of the branched covering construction, in order to aid and clarify the understanding of how these structures can be used in quantum gravity to realize the topological nature of the spacetime foam.
Fields of Study & Subjects
Geometric and Algebraic Topology
Noncommutative and Quantum Gravity Theories
Relativity and Gravitational Theory
Publication details
- Journal / source
- International Journal of Topology
- Volume
- 3
- Issue
- 1
- Pages
- 5–5
- Publication date
- 4 March 2026
- Language
- EN