Characterization of metric spaces with a metric fundamental class

Autor:	Marti, Denis, Soultanis, Elefterios
Rok vydání:	2024
Předmět:	Mathematics - Metric Geometry Mathematics - Differential Geometry 53C23 53C65 (Primary) 49Q15 28A75 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We consider three conditions on metric manifolds with finite volume: (1) the existence of a metric fundamental class, (2) local index bounds for Lipschitz maps, and (3) Gromov--Hausdorff approximation with volume control by bi-Lipschitz manifolds. Condition (1) is known for metric manifolds satisfying the LLC condition by work of Basso--Marti--Wenger, while (3) is known for metric surfaces by work of Ntalampekos--Romney. We prove that for metric manifolds with finite Nagata dimension, all three conditions are equivalent and that without assuming finite Nagata dimension, (1) implies (2) and (3) implies (1). As a corollary we obtain a generalization of the approximation result of Ntalampekos--Romney to metric manifolds of dimension $n\ge 2$, which have the LLC property and finite Nagata dimension. Comment: 25 pages, comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.15794 Zobrazit plný text záznamu View this record from Arxiv