Euler-like vector fields, deformation spaces and manifolds with filtered structure
Abstract
The first purpose of this note is to comment on a recent article of Bursztyn, Lima and Meinrenken, in which it is proved that if M is a smooth submanifold of a manifold V, then there is a bijection between germs of tubular neighborhoods of M and germs of "Euler-like" vector fields on V. We shall explain how to approach this bijection through the deformation to the normal cone that is associated to the embedding of M into V. The second purpose is to study generalizations to smooth manifolds equipped with Lie filtrations. Following in the footsteps of several others, we shall define a deformation to the normal cone that is appropriate to this context, and relate it to Euler-like vector fields and tubular neighborhood embeddings.
Cite
@article{arxiv.1611.05312,
title = {Euler-like vector fields, deformation spaces and manifolds with filtered structure},
author = {Ahmad Reza Haj Saeedi Sadegh and Nigel Higson},
journal= {arXiv preprint arXiv:1611.05312},
year = {2018}
}
Comments
Final version, to appear in Documenta Mathematica, 2018