Geometric Topology in Dimensions 2 and 3

Geometric Topology in Dimensions 2 and 3
Author: E.E. Moise
Publisher: Springer Science & Business Media
Total Pages: 272
Release: 2013-06-29
Genre: Mathematics
ISBN: 1461299063

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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.

Geometric Topology

Geometric Topology
Author: James C. Cantrell
Publisher: Elsevier
Total Pages: 713
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483271315

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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.

The Geometric Topology of 3-manifolds

The Geometric Topology of 3-manifolds
Author: R. H. Bing
Publisher: American Mathematical Soc.
Total Pages: 250
Release: 1983-12-31
Genre: Mathematics
ISBN: 0821810405

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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.

Handbook of Geometric Topology

Handbook of Geometric Topology
Author: R.B. Sher
Publisher: Elsevier
Total Pages: 1145
Release: 2001-12-20
Genre: Mathematics
ISBN: 0080532853

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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.

Algebraic and Geometric Topology

Algebraic and Geometric Topology
Author: R. James Milgram
Publisher: American Mathematical Soc.
Total Pages: 332
Release: 1978-12-31
Genre: Mathematics
ISBN: 9780821867907

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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.

Geometric topology

Geometric topology
Author: William Hilal Kazez
Publisher: American Mathematical Soc.
Total Pages: 622
Release: 1996-10-22
Genre: Mathematics
ISBN: 9780821806548

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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.

Selected Applications of Geometry to Low-Dimensional Topology

Selected Applications of Geometry to Low-Dimensional Topology
Author: Michael H. Freedman
Publisher: American Mathematical Soc.
Total Pages: 93
Release: 1990
Genre: Mathematics
ISBN: 0821870009

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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

Three-dimensional Geometry and Topology
Author: William P. Thurston
Publisher: Princeton University Press
Total Pages: 340
Release: 1997
Genre: Mathematics
ISBN: 9780691083049

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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.