Lipschitz homotopy convergence of Alexandrov spaces

2017/04/28 by Ayato Mitsuishi, Mitsuishi, Ayato, Takao Yamaguchi +1
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Advanced Topology and Set Theory #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1704.08789

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.

Related

• Lipschitz homotopy convergence of Alexandrov spaces II
• Good coverings of Alexandrov spaces
• Lipschitz continuity of harmonic maps between Alexandrov spaces
• Homotopy lifting property of an e^ε-Lipschitz and co-Lipschitz map
• The coincidence of the current homology and the measure homology via a new topology on spaces of Lipschitz maps