Geometric Topology in Dimensions 2 and 3
Author : Edwin E. Moise
Publisher :
Page : 262 pages
File Size : 19,62 MB
Release : 1977
Category : Homeomorphisms
ISBN : 9783540902201
Author : Edwin E. Moise
Publisher :
Page : 262 pages
File Size : 19,62 MB
Release : 1977
Category : Homeomorphisms
ISBN : 9783540902201
Author : E.E. Moise
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 21,18 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 1461299063
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.
Author : R. H. Bing
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 26,86 MB
Release : 1983-12-31
Category : Mathematics
ISBN : 0821810405
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.
Author : James C. Cantrell
Publisher : Elsevier
Page : 713 pages
File Size : 18,39 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483271315
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.
Author : Edwin E. Moise
Publisher :
Page : pages
File Size : 25,43 MB
Release : 1977
Category :
ISBN :
Author : R.B. Sher
Publisher : Elsevier
Page : 1145 pages
File Size : 50,40 MB
Release : 2001-12-20
Category : Mathematics
ISBN : 0080532853
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.
Author : R. James Milgram
Publisher : American Mathematical Soc.
Page : 332 pages
File Size : 24,15 MB
Release : 1978-12-31
Category : Mathematics
ISBN : 9780821867907
Contains sections on Structure of topological manifolds, Low dimensional manifolds, Geometry of differential manifolds and algebraic varieties, $H$-spaces, loop spaces and $CW$ complexes, Problems.
Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 20,43 MB
Release : 2011-06-27
Category : Mathematics
ISBN : 0817681221
The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.
Author : L.C. Glaser
Publisher : Springer
Page : 472 pages
File Size : 11,62 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540374124
Author : William P. Thurston
Publisher : Princeton University Press
Page : 340 pages
File Size : 15,33 MB
Release : 1997
Category : Mathematics
ISBN : 9780691083049
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.