Geometric Topology in Dimensions 2 and 3
Author | : Edwin E. Moise |
Publisher | : |
Total Pages | : 262 |
Release | : 1977 |
Genre | : Homeomorphisms |
ISBN | : 9783540902201 |
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Author | : Edwin E. Moise |
Publisher | : |
Total Pages | : 262 |
Release | : 1977 |
Genre | : Homeomorphisms |
ISBN | : 9783540902201 |
Author | : E.E. Moise |
Publisher | : Springer Science & Business Media |
Total Pages | : 272 |
Release | : 2013-06-29 |
Genre | : 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. |
Total Pages | : 250 |
Release | : 1983-12-31 |
Genre | : 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 |
Total Pages | : 713 |
Release | : 2014-05-10 |
Genre | : 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 | : |
Total Pages | : |
Release | : 1977 |
Genre | : |
ISBN | : |
Author | : R.B. Sher |
Publisher | : Elsevier |
Total Pages | : 1145 |
Release | : 2001-12-20 |
Genre | : 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. |
Total Pages | : 332 |
Release | : 1978-12-31 |
Genre | : 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 |
Total Pages | : 433 |
Release | : 2011-06-27 |
Genre | : 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 |
Total Pages | : 472 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540374124 |
Author | : William P. Thurston |
Publisher | : American Mathematical Society |
Total Pages | : 337 |
Release | : 2023-06-16 |
Genre | : Mathematics |
ISBN | : 1470474743 |
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.