The Realization of 3D Topological Spaces Branched Over Graphs

2025/08/12 by Christopher L Duston, Duston, Christopher L
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Black Holes and Theoretical Physics #Advanced Mathematical Theories and Applications

paper · pdf · doi:10.48550/arxiv.2508.09026

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 topological spaces branched over several graphs are 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.

Citations

• Persistent Homology: A Pedagogical Introduction with Biological Applications
• A Comprehensive Review of the Mapper Algorithm, a Topological Data Analysis Technique, and Its Applications Across Various Fields (2007-2025)
• The Large Scale Structure of Space-Time
• Metrics on End-Periodic Manifolds as Models for Dark Matter
• Gravitational sources induced by exotic smoothness and fermions as knot complements
• The Fundamental Group of a Spatial Section Represented by a Topspin\n Network
• Introduction to high dimensional knots
• The topology of the universe: the biggest manifold of them all

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