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arXiv · 2506.12054

Interacting Geodesics on Discrete Manifolds

Oliver Knill
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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.

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Oliver Knill. 2025-05-30. Interacting Geodesics on Discrete Manifolds. https://arxiv.org/abs/2506.12054

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