On a link criterion for Lipschitz normal embeddings among definable sets

Nguyen Xuan Viet Nhan

Mathematische Nachrichten, 2023, vol. 296, issue 7, 2958-2974

Abstract: 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,+,.)$(\mathbb {R}, + , .)$. We 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.

Date: 2023
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