Lectures on surfaces : (almost) everything you wanted to know about them
Katok, Anatole
Lectures on surfaces : (almost) everything you wanted to know about them by Anatole Katok and Vaughn Climenhaga - Hyderabad : Universities Press, ©2008 - xv, 286 p. : ill. ; 22 cm. - Student mathematical library ; v. 46 . - Student mathematical library ; v. 46. .
Includes bibliographical references (p. 271-274) and index.
Chapter 1. Various ways of representing surfaces and basic examples Chapter 2. Combinatorial structure and topological classification of surfaces Chapter 3. Differentiable structure on surfaces: Real and complex Chapter 4. Riemannian metrics and geometry of surfaces Chapter 5. Topology and smooth structure revisited
Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. At the same time, many of those notions appear in a technically simpler and more graphic form than in their general ""natural"" settings. The first, primarily expository, chapter introduces many of the principal actors--the round sphere, flat torus, Möbius strip, Klein bottle, elliptic plane, etc.--as well as various methods of describing surfaces, beginning with the t.
9781470454821
Surfaces.
516 / KAT-L
Lectures on surfaces : (almost) everything you wanted to know about them by Anatole Katok and Vaughn Climenhaga - Hyderabad : Universities Press, ©2008 - xv, 286 p. : ill. ; 22 cm. - Student mathematical library ; v. 46 . - Student mathematical library ; v. 46. .
Includes bibliographical references (p. 271-274) and index.
Chapter 1. Various ways of representing surfaces and basic examples Chapter 2. Combinatorial structure and topological classification of surfaces Chapter 3. Differentiable structure on surfaces: Real and complex Chapter 4. Riemannian metrics and geometry of surfaces Chapter 5. Topology and smooth structure revisited
Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. At the same time, many of those notions appear in a technically simpler and more graphic form than in their general ""natural"" settings. The first, primarily expository, chapter introduces many of the principal actors--the round sphere, flat torus, Möbius strip, Klein bottle, elliptic plane, etc.--as well as various methods of describing surfaces, beginning with the t.
9781470454821
Surfaces.
516 / KAT-L