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Geometric Topology in Dimensions 2 and 3 (Graduate Texts in Mathematics 47) Hardcover

ISBN-13: 978-0387902203 ISBN-10: 0387902201 Edition: 1st

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Product Details

  • Hardcover: 262 pages
  • Publisher: Springer; 1st edition (April 19, 1977)
  • Language: English
  • ISBN-10: 0387902201
  • ISBN-13: 978-0387902203
  • Product Dimensions: 9.4 x 6.5 x 1 inches
  • Shipping Weight: 1.2 pounds
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #4,073,090 in Books (See Top 100 in Books)

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14 of 16 people found the following review helpful By Malcolm on April 16, 2008
Format: Hardcover
Moise's "Geometric Topology in Dimensions 2 and 3" was somewhat of an anachronism even when it was first published in 1977, containing no result from after 1960, and with much of it dating from decades earlier. This introductory text in low-dimensional PL topology is both inadequate as a PL topology book (the standard references are Rourke and Sanderson or Hudson for this now-disused subject) and hopelessly outdated as a 3-manifold topology book. But it does have one major saving grace: It contains just about the only modern and complete coverage of classical theorems such as the Hauptvermutung and triangularization theorem of Rado that are frequently cited but not proved.

The main topics in 2-dimensions are the Jordan Curve Theorem, the Schoenflies Theorem, Rado's triangularization theorem for 2-manifolds (i.e., topological 2-manifolds are PL), the Hauptvermutung (i.e., any 2 triangularizations are PL equivalent), and the well-known classification of compact 2-manifolds. There are also chapters on PL approximations of homeomorphisms, tame imbeddings, and homeomorphisms of Cantor sets. In 3 dimensions the highlights are the PL Schoenflies Theorem (the originally conjectured topological version is false), the Loop Theorem and the Dehn Lemma, PL approximations, triangularization of 3-manifolds, and the Hauptvermutung, the latter 2 being the culmination of the last 100 pages of the book. There's also an entertaining account of Antoine's wild sphere imbedding and Stallings's counterexample for a simpler version of the Loop Theorem.
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