The euclidean plane -- The hyperbolic plane -- The 2-dimensional sphere -- Gluing constructions -- Gluing examples -- Tessellations -- Group actions and fundamental domains -- The Farey tessellation and circle packing -- The 3-dimensional hyperbolic space -- Kleinian groups -- The figure-eight knot complement -- Geometrization theorems in dimension 3.
Summary
"The study of 3-dimensional 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 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments."--BOOK JACKET.
