Lectures on surfaces : (almost) everything you wanted to know about them /
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. The first chapter introduces many of the principal actors--the round sp...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I. : [Philadelphia] :
American Mathematical Society ; Mathematics Advances Study Semesters,
c2008.
|
| Series: | Student mathematical library;
v. 46. |
| Subjects: |
MARC
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| 100 | 1 | |a Katok, A. B. | |
| 245 | 1 | 0 | |a Lectures on surfaces : |b (almost) everything you wanted to know about them / |c Anatole Katok, Vaughn Climenhaga. |
| 260 | |a Providence, R.I. : |b American Mathematical Society ; |a [Philadelphia] : |b Mathematics Advances Study Semesters, |c c2008. | ||
| 300 | |a xv, 286 p. : |b ill. ; |c 22 cm. | ||
| 490 | 1 | |a Student mathematical library ; |v v. 46 | |
| 520 | |a 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. The first 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 traditional representations by equations in three-dimensional space, proceeding to parametric representation, and representation as factor spaces. It concludes with a discussion of the metric geometry of surfaces and the associated isometry groups. Subsequent chapters introduce fundamental mathematical structures--topological, combinatorial (piecewise-linear), smooth, Riemannian (metric), and complex--in the specific context of surfaces. The focal point of the book is the Euler characteristic, which appears in many different guises and ties together concepts from combinatorics, algebraic topology, Morse theory, ordinary differential equations, and Riemannian geometry. The repeated appearance of the Euler characteristic provides both a unifying theme and an illustration of the notion of an invariant in all those theories.--From publisher's description. | ||
| 504 | |a Includes bibliographical references (p. 271-274) and index. | ||
| 505 | 0 | |a 1. Various ways of representing surfaces and basic examples -- 2. Combinatorial structure and topological classification of surfaces -- 3. Differentiable structure on surfaces: real and complex -- 4. Riemannian metrics and geometry of surfaces -- 5. Topology and smooth structure revisited. | |
| 650 | 0 | |a Surfaces. | |
| 700 | 1 | |a Climenhaga, Vaughn, |d 1982- |4 aut | |
| 830 | 0 | |a Student mathematical library; |v v. 46. | |
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