2016;
386 pp;
Hardcover

MSC: Primary 57; 92; 94;

Print ISBN: 978-1-4704-2535-7

Product Code: MBK/96

List Price: $69.00

Individual Member Price: $55.20

**Electronic ISBN: 978-1-4704-2819-8
Product Code: MBK/96.E**

List Price: $69.00

Individual Member Price: $55.20

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#### Supplemental Materials

# Knots, Molecules, and the Universe: An Introduction to Topology

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*Erica Flapan*

This book is an elementary introduction to
geometric topology and its applications to chemistry, molecular
biology, and cosmology. It does not assume any mathematical or
scientific background, sophistication, or even motivation to study
mathematics. It is meant to be fun and engaging while drawing
students in to learn about fundamental topological and geometric
ideas. Though the book can be read and enjoyed by nonmathematicians,
college students, or even eager high school students, it is intended
to be used as an undergraduate textbook.

The book is divided into three parts corresponding to the three
areas referred to in the title. Part 1 develops techniques that
enable two- and three-dimensional creatures to visualize possible
shapes for their universe and to use topological and geometric
properties to distinguish one such space from another. Part 2 is an
introduction to knot theory with an emphasis on invariants. Part 3
presents applications of topology and geometry to molecular
symmetries, DNA, and proteins. Each chapter ends with exercises that
allow for better understanding of the material.

The style of the book is informal and lively. Though all of the
definitions and theorems are explicitly stated, they are given in an
intuitive rather than a rigorous form, with several hundreds of
figures illustrating the exposition. This allows students to develop
intuition about topology and geometry without getting bogged down in
technical details.

#### Readership

Undergraduate students and instructors interested in elementary topology.

#### Reviews & Endorsements

[T]his is a wonderful introduction to geometry and topology and their applications to the sciences. The book contains a unique collection of topics that might entice young readers to continue their academic careers by learning more about the world of mathematics.

-- Claus Ernst, Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Knots, Molecules, and the Universe: An Introduction to Topology

- Cover Cover11
- Title page iii4
- Contents v6
- Preface xi12
- Acknowledgments xv16
- Part 1. Universes 120
- Chapter 1. An introduction to the shape of the universe 322
- Chapter 2. Visualizing four dimensions 2948
- Chapter 3. Geometry and topology of different universes 4968
- Chapter 4. Orientability 87106
- Chapter 5. Flat manifolds 109128
- Chapter 6. Connected sums of spaces 135154
- Chapter 7. Products of spaces 157176
- Chapter 8. Geometries of surfaces 185204
- Part 2. Knots 213232
- Chapter 9. Introduction to knot theory 215234
- Chapter 10. Invariants of knots and links 239258
- Chapter 11. Knot polynomials 269288
- Part 3. Molecules 289308
- Chapter 12. Mirror image symmetry from different viewpoints 291310
- Chapter 13. Techniques to prove topological chirality 311330
- Chapter 14. The topology and geometry of DNA 329348
- Chapter 15. The topology of proteins 361380
- Index 383402
- Back Cover Back Cover1406