Lipschitz homotopy convergence of Alexandrov spaces
Metric Geometry
2018-08-02 v2 Differential Geometry
Abstract
We introduce the notion of good coverings of metric spaces, and prove that if a metric space admits a good covering, then it has the same locally Lipschitz homotopy type as the nerve complex of the covering. As an application, we obtain a Lipschitz homotopy stability result for a moduli space of compact Alexandrov spaces without collapsing.
Keywords
Cite
@article{arxiv.1704.08789,
title = {Lipschitz homotopy convergence of Alexandrov spaces},
author = {Ayato Mitsuishi and Takao Yamaguchi},
journal= {arXiv preprint arXiv:1704.08789},
year = {2018}
}
Comments
We gave more details for the proofs of Theorems 1.1 and 1.2