On a link criterion for Lipschitz normal embeddings among definable sets
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 . 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.
Keywords
Cite
@article{arxiv.2103.14387,
title = {On a link criterion for Lipschitz normal embeddings among definable sets},
author = {Nhan Nguyen},
journal= {arXiv preprint arXiv:2103.14387},
year = {2022}
}
Comments
There is a little change in the assumption of the function associated to the link, it is required to be Lipschitz instead of being continuous as the previous version. An example in the end of paper showing that this condition is necessary. The title of the paper is also justified