Solutions to open problems in Neeb's recent survey on infinite-dimensional Lie groups

Simple item page
dc.creatorGlockner, Helge
dc.date2008-01-12
dc.date.accessioned2026-07-07T08:54:13Z
dc.date.available2026-07-07T08:54:13Z
dc.descriptionWe solve three open problems concerning infinite-dimensional Lie groups posed in a recent survey article by K.-H. Neeb: (1) There exists a subgroup of some infinite-dimensional Lie group G which does not admit an initial Lie subgroup structure; (2) The pathology cannot occur if G is a direct limit of an ascending sequence of finite-dimensional Lie groups; (3) Every such direct limit group is a ``topological group with Lie algebra'' in the sense of Hofmann and Morris. Moreover, we prove a version of Borel's Theorem announced in the survey, ensuring the existence of compactly supported smooth diffeomorphisms with given Taylor series around a fixed point p (provided the tangent map at p has positive determinant).
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/0801.1919
dc.identifierhttp://arxiv.org/abs/0801.1919
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145850
dc.subjectGroup Theory
dc.subjectDifferential Geometry
dc.subject22E65 (Primary); 58B10 (Secondary)
dc.titleSolutions to open problems in Neeb's recent survey on infinite-dimensional Lie groups
dc.typetext

Files

Collections

arXiv