Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms
Geometric Topology
2025-03-18 v2
Abstract
Cerf and Palais independently proved a remarkable result about extending diffeomorphisms defined on smooth balls in a manifold to global diffeomorphisms of the manifold onto itself. We explain Palais' argument and show how to extend it to the class of homeomorphisms and bi-Lipschitz homeomorphisms. While Palais' argument is surprising, it is elementary and short. However, its extension to bi-Lipschitz homeomorphisms and homeomorphisms requires deep results: the stable homeomorphism and the annulus theorems.
Cite
@article{arxiv.2404.13508,
title = {Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms},
author = {Paweł Goldstein and Zofia Grochulska and Piotr Hajłasz},
journal= {arXiv preprint arXiv:2404.13508},
year = {2025}
}