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Author: E.E. Moise Publisher: 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.
Author: James C. Cantrell Publisher: 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.
Author: R. H. Bing Publisher: 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.
Author: R.B. Sher Publisher: 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.
Author: Michael H. Freedman Publisher: 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.
Author: William Hilal Kazez Publisher: American Mathematical Soc. ISBN: 9780821806548 Category : Mathematics Languages : en Pages : 622
Book Description
This is Part 1 of a two-part volume reflecting the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August. The texts include research and expository articles and problem sets. The conference covered a wide variety of topics in geometric topology. Features: Kirby's problem list, which contains a thorough description of the progress made on each of the problems and includes a very complete bibliography, makes the work useful for specialists and non-specialists who want to learn about the progress made in many areas of topology. This list may serve as a reference work for decades to come. Gabai's problem list, which focuses on foliations and laminations of 3-manifolds, collects for the first time in one paper definitions, results, and problems that may serve as a defining source in the subject area.
Author: William P. Thurston Publisher: 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.
Author: R. James Milgram Publisher: American Mathematical Soc. ISBN: 9780821867907 Category : Mathematics Languages : en Pages : 332
Book Description
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.