Hilbert's fifth problem for local groups

• 成果类型: Article
• 署名作者: Goldbring, Isaac
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 1269-1314
• 关键词: cancellative semigroups; MANIFOLDS

摘要

We solve Hilbert's fifth problem for local groups: every locally euclidean local group is locally isomorphic to a Lie group. Jacoby claimed a proof of this in 1957, but this proof is seriously flawed. We use methods from nonstandard analysis and model our solution after a treatment of Hilbert's fifth problem for global groups by Hirschfeld.