Monotone Mappings of Compact 3-manifolds PDF Download

Author: Alden Halbert Wright
Publisher:
ISBN:
Category : Algebraic topology
Languages : en
Pages : 190

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Author: R. H. Bing
Publisher: American Mathematical Soc.
ISBN: 9780821810477
Category : Mathematics
Languages : en
Pages : 1702

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Book Description
A powerful mathematician and a great problem solver, R. H. Bing laid the foundation for a number of areas of topology. Many of his papers have continued to serve as a source of major theoretical developments and concrete applications in recent years. One outstanding example was Michael H. Freedman's use of Bing's Shrinking Criterion to solve the four-dimensional Poincaré Conjecture. This two-volume set brings together over one hundred of Bing's research, expository, andmiscellaneous papers. These works range over a great variety of topics in topology, including the topology of manifolds, decomposition spaces, continua, metrization, general topology, and geometric topology. In addition, there are a number of papers in the areas of convex functions, linearity, and conformalvarieties. The introductory section in the first volume provides historical background on Bing's life and achievements. This collection will appeal to mathematicians in all areas, and especially those in topology, as well as students, historians, and educators in the mathematical sciences, for it provides a complete historical summary of the mathematical events in the life of the man and the mathematician, R. H. Bing.

Author: Danny Calegari
Publisher: Oxford University Press on Demand
ISBN: 0198570082
Category : Mathematics
Languages : en
Pages : 378

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Book Description
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.

Author: R. H. Bing
Publisher:
ISBN:
Category : Manifolds (Mathematics)
Languages : en
Pages : 38

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Book Description
This is a summary of four Colloquium Lectures given at the meeting of the American Mathematical Society in Laramie in 1970. The first section discusses the recent solution of the monotone mapping theorem. The second discusses difficulty and headway in extending results about 3-manifolds to those of higher dimensions. The last two sections discuss approximation theorems and their applications. (Author).

Author: R.F. Dickman
Publisher: Springer
ISBN: 3540379487
Category : Mathematics
Languages : en
Pages : 297

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Author: Marion Kirkland Fort
Publisher:
ISBN:
Category : Algebraic topology
Languages : en
Pages : 280

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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 256

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Book Description

Author: Steve Armentrout
Publisher: American Mathematical Soc.
ISBN: 0821818074
Category : Decomposition (Mathematics)
Languages : en
Pages : 76

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Book Description

Author: Jean-Pierre Otal
Publisher: American Mathematical Soc.
ISBN: 9780821821534
Category : Mathematics
Languages : en
Pages : 150

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Book Description
For graduate students familiar with low-dimensional topology and researchers in geometry and topology, Otal (CNRS-UMR 128, Lyon) offers a complete proof of Thurston's hyperbolization theorem for 3-manifolds that fiber as surface bundles. The original Le Theoreme d'Hyperbolisation pour les Varietes de Dimension 3, published by the French Mathematical Society in 1996, has been translated by Leslie D. Kay. c. Book News Inc.

Author: Katsuro Sakai
Publisher: Springer Science & Business Media
ISBN: 443154397X
Category : Mathematics
Languages : en
Pages : 539

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Book Description
This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be useful in graduate classes or seminars. Researchers should also find this book very helpful, because it contains many subjects that are not presented in usual textbooks, e.g., dim X × I = dim X + 1 for a metrizable space X; the difference between the small and large inductive dimensions; a hereditarily infinite-dimensional space; the ANR-ness of locally contractible countable-dimensional metrizable spaces; an infinite-dimensional space with finite cohomological dimension; a dimension raising cell-like map; and a non-AR metric linear space. The final chapter enables students to understand how deeply related the two theories are. Simplicial complexes are very useful in topology and are indispensable for studying the theories of both dimension and ANRs. There are many textbooks from which some knowledge of these subjects can be obtained, but no textbook discusses non-locally finite simplicial complexes in detail. So, when we encounter them, we have to refer to the original papers. For instance, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any textbook. The homotopy type of simplicial complexes is discussed in textbooks on algebraic topology using CW complexes, but geometrical arguments using simplicial complexes are rather easy.