No CrossRef data available.
Article contents
Tubular neighbourhoods for submersions of topological manifolds
Published online by Cambridge University Press: 17 April 2009
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Let φ: M → N be a submersion from a metrizable manifold to any (topological) manifold, let B ⊂ M be compact, y є N and C ⊂ φ−1(y) be a compact neighbourhood (in φ−1(y)) of B ∩ φ−1(y). It is proven that there is a neighbourhood U of y in N and an embedding ε: U × C → M such that φε is projection on the first factor, ε(y, x) = x for each x ε C, and B ∩ φ−1 (U) ⊂ ε(U×C). The main application given is to topological foliations, it being shown that if C is a compact regular leaf of a foliation F on M then every neighbourhood of C contains a saturated neighbourhood which is the union of compact regular leaves of F.
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1973
References
[1]Edwards, Robert D. and Kirby, Robion C., “Deformations of spaces of imbeddings”, Ann. of Math. (2) 93 (1971), 63–88.CrossRefGoogle Scholar
[2]Gauld, David B., “Submersions and foliations of topological manifolds”, Math. Chronicle 1 (1971), 139–146.Google Scholar
[3]Palais, Richard S., A global formulation of the Lie theory of transformation groups (Mem. Amer. Math. Soc. 22. Amer. Math. Soc., Providence, Rhode Island, 1957).CrossRefGoogle Scholar
[4]Short, Donald R. and Smith, J. Wolfgang, “A Vietoris-Begle theorem for submersions”, Indiana Univ. Math. J. 20 (1970/1971), 327–336.CrossRefGoogle Scholar
[5]Smith, J. Wolfgang, “Submersions with p-connected fibers”, Math. Z. 121 (1971), 288–294.CrossRefGoogle Scholar
You have
Access