Embeddings in Manifolds

Robert J Daverman,Gerard A Venema,

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AUTEUR Robert J Daverman,Gerard A Venema,
ISBN 9780821836972

Embeddings in Manifolds...

This article gives a short guide to the problem of classifying embeddings of closed manifolds into Euclidean space or the sphere up to isotopy (i.e., to the Knotting Problem of Remark for embeddings of general manifolds into or).After making some general remarks and giving references, in Section 2 we record some of the dimension ranges where no knotting is possible, i.e. where any two. In a later conversation with Robert M. Solovay, Nash mentioned of a fault in the original argument in deriving the sufficing value of the dimension of the embedding space for the case of non-compact manifolds. The Nash embedding theorem is a global theorem in the sense that the whole manifold is embedded into R n. 03/04/ · First, Embeddings in Manifolds relies heavily on the (apparently out-of-print) classic Introduction to Piecewise-Linear Topology by Colin P. Rourke and B. J. Sanderson (Springer-Verlag, ). Indeed, the serious reader is advised to have a copy of Rourke and Sanderson’s book at hand; Embeddings on Manifolds makes.[11] R. Greene, Isometric embeddings of Riemannian and pseudo-Riemannian manifolds, Memoirs of the American Mathematical Society, No. 97, [12] M. Embeddings, isotopy and stability of Banach manifolds. K. D. Elworthy · Compositio Mathematica (). Volume: 24, Issue: 2, page ; ISSN: X. By topological lacet we mean the embedding, with self-intersections, of a closed curve in a 2-manifold, such that (1) all self-intersections are.