The geometric topology of 3-manifolds / R. H. Bing

Bibliogr. p. 229-233. Index

This book has as one of its main purposes to give an understandable proof of the side approximation theorem. There are a number of topics that are related to the side approximation theorem which are included in the book as well. These include wild surfaces (Chapters IV, VI), the Schoenflies theorem (Chapters III, V, XIV), Dehn's lemma (Chapters XV, XVI), and the loop theorem (Chapter XVII). An attempt has been made to make the book relatively self-contained. Some topics from PL topology, homotopy theory, and homology theory have been included. Since the main interest is in 3-manifolds, only those aspects of these topics which impinge on the study of 3-manifolds are included. The philosophy of the book is the development of mathematics from the specific to the general. The material is traditional and an attempt has been made to make the presentation straightforward and down-to-earth.
This book is a classic in the study of the geometric topology of 3-manifolds. Virtually everything that is known about 3-manifolds from the standpoint of geometric topology is included here. One has wild surfaces, the Schoenflies theorem, triangulation, Dehn's lemma, the shrinking criterion, linking, the loop theorem, covering spaces, as well as the important side approximation theorem. Many of these results are applications of the side approximation theorem. ... The book would be suitable as a text for a second graduate course in topology. The exposition is excellent and the student (not to say the teacher) would find the book understandable and stimulating. (MathSciNet)