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arXiv · 1611.05312

Euler-like vector fields, deformation spaces and manifolds with filtered structure

Ahmad Reza Haj Saeedi Sadegh·Nigel Higson
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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.

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Ahmad Reza Haj Saeedi Sadegh, Nigel Higson. 2016-11-16. Euler-like vector fields, deformation spaces and manifolds with filtered structure. https://arxiv.org/abs/1611.05312

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