**Student Mathematical Library**

Volume: 60;
2011;
314 pp;
Softcover

MSC: Primary 14; 30; 32; 37; 53; 51;

Print ISBN: 978-0-8218-5368-9

Product Code: STML/60

List Price: $49.00

Individual Price: $39.20

**Electronic ISBN: 978-1-4704-1223-4
Product Code: STML/60.E**

List Price: $49.00

Individual Price: $39.20

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#### Supplemental Materials

# Mostly Surfaces

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*Richard Evan Schwartz*

This book presents a number of topics related to surfaces, such as Euclidean, spherical and hyperbolic geometry, the fundamental group, universal covering surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. The main idea is to get to some interesting mathematics without too much formality. The book also includes some material only tangentially related to surfaces, such as the Cauchy Rigidity Theorem, the Dehn Dissection Theorem, and the Banach–Tarski Theorem.

The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis.

#### Table of Contents

# Table of Contents

## Mostly Surfaces

- Cover Cover11 free
- Title page i2 free
- Contents iii4 free
- Preface xi12 free
- Book overview 116 free
- Part 1. Surfaces and topology 1934
- Definition of a surface 2136
- The gluing construction 3146
- The fundamental group 4358
- Examples of fundamental groups 5368
- Covering spaces and the deck group 6580
- Existence of universal covers 7994
- Part 2. Surfaces and geometry 85100
- Euclidean geometry 87102
- Spherical geometry 103118
- Hyperbolic geometry 115130
- Riemann metrics on surfaces 133148
- Hyperbolic surfaces 143158
- Part 3. Surfaces and complex analysis 161176
- A primer on complex analysis 163178
- Disk and plane rigidity 177192
- The Schwarz-Christoffel transformation 183198
- Riemann surfaces and uniformization 195210
- Part 4. Flat cone surfaces 205220
- Flat cone surfaces 207222
- Translation surfaces and the Veech group 221236
- Part 5. The totality of surfaces 237252
- Continued fractions 239254
- Teichmüller space and moduli space 251266
- Topology of Teichmüller space 263278
- Part 6. Dessert 273288
- The Banach Tarski theorem 275290
- Dehn’s dissection theorem 287302
- The Cauchy rigidity theorem 295310
- Bibliography 309324
- Index 311326 free
- Back Cover Back Cover1330

#### Readership

Undergraduate students interested in geometry and topology of surfaces.

#### Reviews

The book contains a lot of interesting basic and more advanced material which is presented in a nice, intuitive yet rigorous way, and, as such, is perfectly suited as an accompanying text or additional reading for a first course on topology or as a basis for a student seminar.

-- Mathematical Reviews

This is a novel, eclectic, and ambitious collection of geometric and topological topics developed as they relate to surfaces ... a terrific volume. Highly recommended.

-- CHOICE

...a delightful reading. Schwartz gives a beautiful, careful exposition of some of the most elegant ideas, theorems, and proofs in the theory of surfaces. It's an ideal book for casual reading in spare mathematical moments.

-- MAA Reviews

This highly readable book is an excellent introduction to the theory of surfaces, covering a wide variety of topics with references for further reading. Each chapter contains numerous exercises on the material to get the reader thinking about the subjects covered. There are also many diagrams to aid the reader in understanding the material.

-- Alastair Fletcher, Zentralblatt MATH