Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
neat embedding; Hilbert manifold; manifold with smooth boundary; normal bundle manifold; collar neighbourhood
neat embedding; Hilbert manifold; manifold with smooth boundary; normal bundle manifold; collar neighbourhood
Summary:
In this paper we prove the existence of a closed neat embedding of a Hausdorff paracompact Hilbert manifold with smooth boundary into $H \times [0, + \infty)$, where $H$ is a Hilbert space, such that the normal space in each point of a certain neighbourhood of the boundary is contained in $H \times \{ 0 \}$. Then, we give a neccesary and sufficient condition that a Hausdorff paracompact topological space could admit a differentiable structure of class $\infty$ with smooth boundary.
References:
[1] R. Abraham: Lectures of Smale Differential Topology. Columbia University, New York, 1962.
[2] S. Armas-Gómez J. Margalef-Roig E. Outerelo-Domínguez E. Padrón-Fernández: Embedding of an Urysohn differentiable manifold with corners in a real Banach space. Winter School of Geometry and Physics held in SRNI (January, 1991, Czechoslovak).
[3] H. Cartan: Sur les Rétractions d’une varieté. C.R. Acad. Sc. Paris, A. 303, Serie I, n. 14, 1986, p. 715. MR 0870703 | Zbl 0609.32021
[4] J. Eells K.D. Elworthy: Open embeddings of certain Banach manifolds. Ann. of Math. 91, 1970, 465–485. MR 0263120
[5] R. Godement: Théorie des faisceaux. Hermann, Paris, 1958. MR 0102797 | Zbl 0080.16201
[6] J. Margalef-Roig E. Outerelo-Domínguez: Topología diferencial. C.S.I.C., Madrid, 1988. MR 0939168
[7] J. Margalef-Roig E. Outerelo-Domínguez: On Retraction of Manifolds with corners. (to appear). MR 1303795
[8] J.H. McAlpin: Infinite dimensional manifolds and Morse theory. Ph.D. Thesis, Columbia University, New York, 1965.
[9] R.E. Stong: Notes on Cobordism Theory. Princeton University Press, 1968. MR 0248858 | Zbl 0181.26604
Search
Partner of
