Geometric Topology in Dimensions 2 and 3

Geometric Topology in Dimensions 2 and 3
Author :
Publisher : Springer Science & Business Media
Total Pages : 272
Release :
ISBN-10 : 9781461299066
ISBN-13 : 1461299063
Rating : 4/5 (66 Downloads)

Book Synopsis Geometric Topology in Dimensions 2 and 3 by : E.E. Moise

Download or read book Geometric Topology in Dimensions 2 and 3 written by E.E. Moise and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 in Dimensions 2 and 3 Related Books

Geometric Topology in Dimensions 2 and 3
Language: en
Pages: 272
Authors: E.E. Moise
Categories: Mathematics
Type: BOOK - Published: 2013-06-29 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

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 fa
Handbook of Geometric Topology
Language: en
Pages: 1145
Authors: R.B. Sher
Categories: Mathematics
Type: BOOK - Published: 2001-12-20 - Publisher: Elsevier

DOWNLOAD EBOOK

Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manif
A First Course in Geometric Topology and Differential Geometry
Language: en
Pages: 433
Authors: Ethan D. Bloch
Categories: Mathematics
Type: BOOK - Published: 2011-06-27 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illust
Low-Dimensional Geometry
Language: en
Pages: 403
Authors: Francis Bonahon
Categories: Mathematics
Type: BOOK - Published: 2009-07-14 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number
Topology and Geometry
Language: en
Pages: 580
Authors: Glen E. Bredon
Categories: Mathematics
Type: BOOK - Published: 1993-06-24 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and d