
Preface  Table of Contents  Supplementary Material 
Student Mathematical Library 2009; 384 pp; softcover Volume: 49 ISBN10: 082184816X ISBN13: 9780821848166 List Price: US$54 Institutional Members: US$43.20 All Individuals: US$43.20 Order Code: STML/49 See also: Hamilton's Ricci Flow  Bennett Chow, Peng Lu and Lei Ni Low Dimensional Topology  Tomasz S Mrowka and Peter S Ozsvath Lectures on Surfaces: (Almost) Everything You Wanted to Know about Them  Anatole Katok and Vaughn Climenhaga  The study of 3dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. LowDimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified. This book is published in cooperation with IAS/Park City Mathematics Institute. Readership Undergraduate students interested in topology and/or geometry of lowdimensional manifolds, particularly 3manifolds. Reviews "...an essential book, if just because no other yet competes for this crucial niche, but also happily excellent in every respectpassionately told, expertly rendered, exquisitely organized, and sumptuously illustrated. ... Essential."  CHOICE Magazine 


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