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The Geometric Topology of 3-Manifolds
R. H. Bing
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Colloquium Publications
1983; 238 pp; softcover
Volume: 40
Reprint/Revision History:
fourth printing 2001
ISBN-10: 0-8218-1040-5
ISBN-13: 978-0-8218-1040-8
List Price: US$90
Member Price: US$72
Order Code: COLL/40
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This book belongs in both graduate and undergraduate libraries as a useful reference for students and researchers in topology. It is directed toward mathematicians interested in geometry who have had at least a beginning course in topology. It should provide the reader with a better understanding of the physical properties of Euclidean 3-space--the space in which we presume we live. The reader should learn of some unsolved problems that continue to baffle reseachers.

The most profound result in the volume is the side approximation theorem. However, some of the preliminary results and some of the applications may be used more frequently for reference.

Table of Contents

  • Planar complexes
  • PL planar maps
  • The Schoenflies theorem
  • Wild 2-spheres
  • The generalized Schoenflies theorem
  • The fundamental group
  • Mapping onto spheres
  • Linking
  • Separation
  • Pulling back feelers
  • Intersections of surfaces with \(1\)-simplexes
  • Intersections of surfaces with skeleta
  • Side approximation theorem
  • The PL Schoenflies theory for \(R^3\)
  • Covering spaces
  • Dehn's lemma
  • Loop theorem
  • Related results
  • AppendiX: Some standard results in topology
  • References
  • Index
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