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arXiv · 2209.12736

Gromov-Hausdorff metrics and dimensions of Lorentzian length spaces

Olaf Müller
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Abstract

We construct analoga of Gromov-Hausdorff space for Lorentzian distances and show a Gromov precompactness result for one of them. After calculating the Dushnik-Miller dimension of Minkowski spaces (of manifold dimension larger than 2) to be countable infinity, we define a dimension for ordered sets recovering the correct manifold dimension, obtain an obstruction for existence of injective monotonous maps between Lorentzian length spaces, induce functorial pseudo-metrics on Cauchy subsets that in the spacetime case coincide with the Riemannian ones, and prove existence of anti-Lipschitz Cauchy functions with a given Cauchy zero locus, a fundamental ingredient for the Sormani-Vega null distance.

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Olaf Müller. 2022-09-26. Gromov-Hausdorff metrics and dimensions of Lorentzian length spaces. https://arxiv.org/abs/2209.12736

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