Interacting Geodesics on Discrete Manifolds

TL;DR

This paper introduces a model of multiple particles moving deterministically on a discrete manifold, where particles follow geodesics and interact on shared facets, leading to reversible space deformations.

Contribution

It defines a novel framework for particle interactions on discrete manifolds using geodesic motion and reversible deformations within the frame bundle.

Findings

Particles move deterministically on geodesics

Interactions occur when particles share a facet

Reversible deformations of space are achieved

Abstract

We define an evolution of multiple particles on a discrete manifold $G$. Each particle alone moves on geodesics and particles can interact if they are on the same facet. They move deterministically and reversibly on the frame bundle $P$ of the abstract simplicial complex $G$. Particles are signed and each is represented by a totally ordered maximal simplex $p \in P$ in $G$. The motion of divisors on $P$ also defines a time dependent reversible deformation of space.