The approximate tubular neighborhood theorem

• 成果类型: Article
• 署名作者: Hughes, B
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3597284
• 发表日期: 2002
• 页码: 867-889
• 关键词: topological manifolds; homeomorphisms; fibrations; SPACES; stratifications

摘要

Skeleta and other pure subsets of manifold stratified spaces are shown to have neighborhoods which are teardrops of stratified approximate fibrations (under dimension and compactness assumptions). In general, the stratified approximate fibrations cannot be replaced by bundles, and the teardrops cannot be replaced by mapping cylinder neighborhoods. Thus, this is the best possible topological tubular neighborhood theorem in the stratified setting.