Embeddings In Manifolds
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Embeddings In Manifolds
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Author : Robert J. Daverman
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-10-14
Embeddings In Manifolds written by Robert J. Daverman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-14 with Mathematics categories.
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.
Embeddings In Manifolds
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Author : Robert J. Daverman
language : en
Publisher:
Release Date : 2009
Embeddings In Manifolds written by Robert J. Daverman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Embeddings (Mathematics) categories.
Embeddings And Immersions
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Author : Masahisa Adachi
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-11-07
Embeddings And Immersions written by Masahisa Adachi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-07 with Mathematics categories.
This book covers fundamental techniques in the theory of -imbeddings and -immersions, emphasizing clear intuitive understanding and containing many figures and diagrams. Adachi starts with an introduction to the work of Whitney and of Haefliger on -imbeddings and -manifolds. The Smale-Hirsch theorem is presented as a generalization of the classification of -imbeddings by isotopy and is extended by Gromov's work on the subject, including Gromov's convex integration theory. Finally, as an application of Gromov's work, the author introduces Haefliger's classification theorem of foliations on open manifolds. Also described here is the Adachi's work with Landweber on the integrability of almost complex structures on open manifolds. This book would be an excellent text for upper-division undergraduate or graduate courses.Nothing provided
Isometric Embeddings Of Riemannian And Pseudo Riemannian Manifolds
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Author : Robert Everist Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 1970
Isometric Embeddings Of Riemannian And Pseudo Riemannian Manifolds written by Robert Everist Greene and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Embeddings (Mathematics) categories.
Proper Embeddings Of Open Manifolds In Euclidean Space
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Author : David Harold Spring
language : en
Publisher:
Release Date : 1967
Proper Embeddings Of Open Manifolds In Euclidean Space written by David Harold Spring and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Differential topology categories.
Topological Embeddings
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Author :
language : en
Publisher: Academic Press
Release Date : 1973-03-30
Topological Embeddings written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-03-30 with Mathematics categories.
Topological Embeddings
Isometric Embedding Of Riemannian Manifolds In Euclidean Spaces
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Author : Qing Han
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-05-21
Isometric Embedding Of Riemannian Manifolds In Euclidean Spaces written by Qing Han and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-21 with MATHEMATICS categories.
The question of the existence of isometric embeddings of Riemannian manifolds in Euclidean space is already more than a century old. This book presents, in a systematic way, results both local and global and in arbitrary dimension but with a focus on the isometric embedding of surfaces in ${\mathbb R} DEG
Isometric Embedding Of Riemannian Manifolds In Euclidean Spaces
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Author : Qing Han
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Isometric Embedding Of Riemannian Manifolds In Euclidean Spaces written by Qing Han and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Algebraic spaces categories.
The question of the existence of isometric embeddings of Riemannian manifolds in Euclidean space is already more than a century old. This book presents, in a systematic way, results both local and global and in arbitrary dimension but with a focus on the isometric embedding of surfaces in ${\mathbb R}^3$. The emphasis is on those PDE techniques which are essential to the most important results of the last century. The classic results in this book include the Janet-Cartan Theorem, Nirenberg's solution of the Weyl problem, and Nash's Embedding Theorem, with a simplified proof by Gunther. The book also includes the main results from the past twenty years, both local and global, on the isometric embedding of surfaces in Euclidean 3-space. The work will be indispensable to researchers in the area. Moreover, the authors integrate the results and techniques into a unified whole, providing a good entry point into the area for advanced graduate students or anyone interested in this subject. The authors avoid what is technically complicated. Background knowledge is kept to an essential minimum: a one-semester course in differential geometry and a one-year course in partial differential equations.
The Embedding Of Homotopy Types Into Manifolds
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Author : John Robert Stallings
language : en
Publisher:
Release Date : 1965
The Embedding Of Homotopy Types Into Manifolds written by John Robert Stallings and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Differential topology categories.
Groups Of Automorphisms Of Manifolds
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Author : D. Burghelea
language : en
Publisher: Springer
Release Date : 2006-11-14
Groups Of Automorphisms Of Manifolds written by D. Burghelea and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.