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Geometric Topology in Dimensions 2 and 3 by E.E. Moise (Paperback, 2013)

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About this product

Product Information

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.

Product Identifiers

Publisher
Springer-Verlag New York Inc.
ISBN-13
9781461299080
eBay Product ID (ePID)
189258084

Product Key Features

Author
E.E. Moise
Publication Name
Geometric Topology in Dimensions 2 and 3
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
2013
Type
Textbook
Number of Pages
262 Pages

Dimensions

Item Height
235mm
Item Width
155mm
Volume
47
Item Weight
427g

Additional Product Features

Title_Author
E.E. Moise
Series Title
Graduate Texts in Mathematics
Country/Region of Manufacture
United States

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