SURFACES AND THREE-MANIFOLDS. Flatland. Gluing. Vocabulary. Orientability. Connected Sums. Products. Flat Manifolds. Orientability vs. Two-Sidedness. GEOMETRIES ON SURFACES. The Sphere. The Hyperbolic Plane. Geometries on Surfaces. The Gauss-Bonnet Formula and the Euler Number. GEOMETRIES ON THREE-MANIFOLDS. Four-Dimensional Space. The Hypersphere. Hyperbolic Space. Geometries on Three-Manifolds I. Bundles. Geometries on Three-Manifolds II. THE UNIVERSE. The Universe. The History of Space. Cosmic Crystallography. Circles in the Sky.
(source: Nielsen Book Data)
Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces. Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behaviour of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe. (source: Nielsen Book Data)