Topological Embeddings
Title | Topological Embeddings PDF eBook |
Author | |
Publisher | Academic Press |
Pages | 333 |
Release | 1973-03-30 |
Genre | Mathematics |
ISBN | 0080873677 |
Topological Embeddings
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.
Evolving Computability
Title | Evolving Computability PDF eBook |
Author | Arnold Beckmann |
Publisher | Springer |
Pages | 375 |
Release | 2015-06-19 |
Genre | Computers |
ISBN | 3319200283 |
This book constitutes the refereed proceedings of the 11th Conference on Computability in Europe, CiE 2015, held in Bucharest, Romania, in June/July 2015. The 26 revised papers presented were carefully reviewed and selected from 64 submissions and included together with 10 invited papers in this proceedings. The conference CiE 2015 has six special sessions: two sessions, Representing Streams and Reverse Mathematics, were introduced for the first time in the conference series. In addition to this, new developments in areas frequently covered in the CiE conference series were addressed in the further special sessions on Automata, Logic and Infinite Games; Bio-inspired Computation; Classical Computability Theory; as well as History and Philosophy of Computing.
Topological Embeddings
Title | Topological Embeddings PDF eBook |
Author | T. Benny Rushing |
Publisher | |
Pages | 316 |
Release | 1973 |
Genre | Plongement topologique |
ISBN |
Library of Congress Subject Headings
Title | Library of Congress Subject Headings PDF eBook |
Author | Library of Congress. Cataloging Policy and Support Office |
Publisher | |
Pages | 1662 |
Release | 2004 |
Genre | Subject headings, Library of Congress |
ISBN |
Library of Congress Subject Headings
Title | Library of Congress Subject Headings PDF eBook |
Author | Library of Congress |
Publisher | |
Pages | 1540 |
Release | 2011 |
Genre | Subject headings, Library of Congress |
ISBN |
Introduction to General Topology
Title | Introduction to General Topology PDF eBook |
Author | K. D. Joshi |
Publisher | New Age International |
Pages | 430 |
Release | 1983 |
Genre | Topology |
ISBN | 9780852264447 |