Embeddings and Immersions of Manifolds in Euclidean Space, Dissertation
Title | Embeddings and Immersions of Manifolds in Euclidean Space, Dissertation PDF eBook |
Author | David Rees Bausum |
Publisher | |
Pages | 100 |
Release | 1974 |
Genre | |
ISBN |
Au temps de Charles X, 1824/1830
Title | Au temps de Charles X, 1824/1830 PDF eBook |
Author | |
Publisher | |
Pages | |
Release | 1972 |
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The Embedding and Immersion of Differential Manifolds in Euclidean Space, with Application to Complex and Quaternionic Projective Spaces
Title | The Embedding and Immersion of Differential Manifolds in Euclidean Space, with Application to Complex and Quaternionic Projective Spaces PDF eBook |
Author | Anthony Leonard JOHNSON |
Publisher | |
Pages | 0 |
Release | 1971 |
Genre | |
ISBN |
Immersions and Embeddings of Manifolds in Euclidean Space
Title | Immersions and Embeddings of Manifolds in Euclidean Space PDF eBook |
Author | Robert David Rigdon |
Publisher | |
Pages | 282 |
Release | 1970 |
Genre | |
ISBN |
Isometric Embeddings of Riemannian and Pseudo-Riemannian Manifolds
Title | Isometric Embeddings of Riemannian and Pseudo-Riemannian Manifolds PDF eBook |
Author | Robert Everist Greene |
Publisher | American Mathematical Soc. |
Pages | 69 |
Release | 1970 |
Genre | Embeddings (Mathematics) |
ISBN | 0821812971 |
Embeddings in Manifolds
Title | Embeddings in Manifolds PDF eBook |
Author | Robert J. Daverman |
Publisher | American Mathematical Soc. |
Pages | 496 |
Release | 2009-10-14 |
Genre | Mathematics |
ISBN | 0821836978 |
A topological embedding is a homeomorphism of one space onto a subspace of another. The book analyzes how and when objects like polyhedra or manifolds embed in a given higher-dimensional manifold. The main problem is to determine when two topological embeddings of the same object are equivalent in the sense of differing only by a homeomorphism of the ambient manifold. Knot theory is the special case of spheres smoothly embedded in spheres; in this book, much more general spaces and much more general embeddings are considered. A key aspect of the main problem is taming: when is a topological embedding of a polyhedron equivalent to a piecewise linear embedding? A central theme of the book is the fundamental role played by local homotopy properties of the complement in answering this taming question. The book begins with a fresh description of the various classic examples of wild embeddings (i.e., embeddings inequivalent to piecewise linear embeddings). Engulfing, the fundamental tool of the subject, is developed next. After that, the study of embeddings is organized by codimension (the difference between the ambient dimension and the dimension of the embedded space). In all codimensions greater than two, topological embeddings of compacta are approximated by nicer embeddings, nice embeddings of polyhedra are tamed, topological embeddings of polyhedra are approximated by piecewise linear embeddings, and piecewise linear embeddings are locally unknotted. Complete details of the codimension-three proofs, including the requisite piecewise linear tools, are provided. The treatment of codimension-two embeddings includes a self-contained, elementary exposition of the algebraic invariants needed to construct counterexamples to the approximation and existence of embeddings. The treatment of codimension-one embeddings includes the locally flat approximation theorem for manifolds as well as the characterization of local flatness in terms of local homotopy properties.
Tight and Taut Immersions of Manifolds
Title | Tight and Taut Immersions of Manifolds PDF eBook |
Author | Thomas E. Cecil |
Publisher | Pitman Advanced Publishing Program |
Pages | 360 |
Release | 1985 |
Genre | Mathematics |
ISBN |