Liftable vector fields, unfoldings and augmentations
  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. 
Juan Jos\'e Nu\~no Ballesteros and Ra\'ul Oset Sinha
math.CV math.AG