Author: Edwin E. MoisePublisher:
ISBN: 9783540902201
Category : Homeomorphisms
Languages : en
Pages : 262
Book Description
Geometric Topology in Dimensions 2 and 3
Author: Edwin E. MoisePublisher:
ISBN: 9783540902201
Category : Homeomorphisms
Languages : en
Pages : 262
Book Description
Geometric Topology in Dimensions 2 and 3
Author: E.E. MoisePublisher: Springer Science & Business Media
ISBN: 1461299063
Category : Mathematics
Languages : en
Pages : 272
Book Description
Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter.
The Geometric Topology of 3-manifolds
Author: R. H. BingPublisher: American Mathematical Soc.
ISBN: 0821810405
Category : Mathematics
Languages : en
Pages : 250
Book Description
Suitable for students and researchers in topology. this work provides the reader with an understanding of the physical properties of Euclidean 3-space - the space in which we presume we live.
Geometric Topology
Author: James C. CantrellPublisher: Elsevier
ISBN: 1483271315
Category : Mathematics
Languages : en
Pages : 713
Book Description
Geometric Topology contains the proceedings of the 1977 Georgia Topology Conference, held at the University of Georgia on August 1977. The book is comprised of contributions from leading experts in the field of geometric topology.These contributions are grouped into four sections: low dimensional manifolds, topology of manifolds, shape theory and infinite dimensional topology, and miscellaneous problems. Subjects discussed under these sections include local spanning missing loops, the structure of generalized manifolds having nonmanifold set of trivial dimension, universal open principal fibrations, and how to build a flexible polyhedral surface. Topologists, geometers, and mathematicians will find the book very interesting and insightful.
Geometric Topology in Dimension 2 and 3
Author: Edwin E. MoiseHandbook of Geometric Topology
Author: R.B. SherPublisher: Elsevier
ISBN: 0080532853
Category : Mathematics
Languages : en
Pages : 1145
Book Description
Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
Geometric Topology
Author: L.C. GlaserPublisher: Springer
ISBN: 3540374124
Category : Mathematics
Languages : en
Pages : 472
Book Description
The Geometry and Topology of Three-Manifolds
Author: William P. ThurstonPublisher: American Mathematical Society
ISBN: 1470474743
Category : Mathematics
Languages : en
Pages : 337
Book Description
William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume IV contains Thurston's highly influential, though previously unpublished, 1977–78 Princeton Course Notes on the Geometry and Topology of 3-manifolds. It is an indispensable part of the Thurston collection but can also be used on its own as a textbook or for self-study.
Selected Applications of Geometry to Low-Dimensional Topology
Author: Michael H. FreedmanPublisher: American Mathematical Soc.
ISBN: 0821870009
Category : Mathematics
Languages : en
Pages : 93
Book Description
Based on lectures presented at Pennsylvania State University in February 1987, this work begins with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceeds to the topology and geometry of foliated 3-manifolds. It also explains why four-dimensional space has special attributes.
Three-dimensional Geometry and Topology
Author: William P. ThurstonPublisher: Princeton University Press
ISBN: 9780691083049
Category : Mathematics
Languages : en
Pages : 340
Book Description
Every mathematician should be acquainted with the basic facts about the geometry of surfaces, of two-dimensional manifolds. The theory of three-dimensional manifolds is much more difficult and still only partly understood, although there is ample evidence that the theory of three-dimensional manifolds is one of the most beautiful in the whole of mathematics. This excellent introductory work makes this mathematical wonderland remained rather inaccessible to non-specialists. The author is both a leading researcher, with a formidable geometric intuition, and a gifted expositor. His vivid descriptions of what it might be like to live in this or that three-dimensional manifold bring the subject to life. Like Poincaré, he appeals to intuition, but his enthusiasm is infectious and should make many converts for this kind of mathematics. There are good pictures, plenty of exercises and problems, and the reader will find a selection of topics which are not found in the standard repertoire. This book contains a great deal of interesting mathematics.