Liftable vector fields, unfoldings and augmentations

TL;DR

This paper investigates liftable vector fields of smooth map-germs, providing methods to derive them from stable unfoldings and exploring their relation to augmentations, with applications to specific singularity families.

Contribution

It introduces a method to obtain liftable vector fields from stable unfoldings and explores their relation to augmentations, advancing the understanding of singularity theory.

Findings

Derived liftable vector fields for the family H_k in Mond's list.

Established a relation between liftable vector fields of stable germs and their augmentations.

Provided a systematic approach to compute liftable vector fields for finite singularity types.

Abstract

We study liftable vector fields of smooth map-germs. We show how to obtain the module of liftable vector fields of any map-germ of finite singularity type from the module of liftable vector fields of a stable unfolding of it. As an application, we obtain the liftable vector fields for the family $H_k$ in Mond's list. We then show the relation between the liftable vector fields of a stable germ and its augmentations.