2021/03/26 by Nhan Nguyen, Nguyen, Nhan
Computer Science · Mathematics · #14B05 #32C05 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2103.14387
openalex publication_date 2021/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
It is known by a result of Mendes and Sampaio that the Lipschitz normal embedding of a subanalytic germ is fully characterized by the Lipschitz normal embedding of its link. In this note, we show that the result still holds for definable germs in any o-minimal structure on (ℝ, + , .). We also give an example showing that for homomorphisms between MD-homologies induced by the identity map, being isomorphic is not enough to ensure that the given germ is Lipschitz normally embedded. This is a negative answer to the question asked by Bobadilla et al. in their paper about Moderately Discontinuous Homology.