Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make this material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces, and three-dimensional manifolds, fixed points, and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting geometrical ideas of topology now(!) rather than later.

### Table of Contents

Preface

Deformations

Knots and Links

Surfaces

Three-Dimensional Manifolds

Fixed Points

The Fundamental Group

Metric and Topological Spaces

Index

About the Author

### About the Author

**Robert Messer** studied mathematics as an undergraduate at the University of Chicago. He wrote his thesis in geometric topology at the University of Wisconsin under D. Russell McMillan, receiving his PhD in 1975. He was a John Wesley Young Research Instructor at Dartmouth College and has taught at Western Michigan University and Vanderbilt University. He has been at Albion College since 1981 where he has served as chair of the department of mathematics and computer science from 1997 to 2002.

In addition to research in topology, he is the author of the textbook* Linear Algebra: Gateway to Mathematics* (1994) and one of the co-authors of *Learning by Discovery: A Lab Manual for Calculus* (MAA, 1993). He helped to organize and coach the Michigan All-Star Math Team for the American Regions Mathematics League Competitions and has served as director of Michigan Mathematics Prize Competition for the Michigan Section of the Mathematical Association of America. He enjoys combinatorics and symmetry of English change ringing as well as traditional American and English country dance.

**Philip Straffin** earned his undergraduate degree in mathematics from Harvard University. He learned knot theory from Ray Lickorish at Cambridge University on a Marshall Scholarship, and received his PhD from the University of California at Berkeley, with a thesis in algebraic topology under Emery Thomas. He has taught at Beloit College since 1970, and served as Chair of Mathematics and Computer Science from 1980 to 1990. He has twice been chosen as Beloit College’s Teacher of the Year, and received the MAA’s Haimo Award for Distinguished College Teaching of Mathematics in 1993.

Professor Straffin has published over 30 research and expository papers, and has won the Allendoerfer Award and the Trevor Evans Award for mathematical exposition from the MAA. His books include: *Topics in the Theory of Voting* (1980) and *Game Theory and Strategy* (MAA, 1993), and edited collections *Political and Related Models* (with Steven Brams and William Lucas, 1983) and *Applications of Calculus* (MAA, 193). He is a member of the American Mathematical Society, the Mathematical Association of America and the Association for Women and Mathematics. For the MAA, he has been Chair of the Wisconsin Section, Editor of the Anneli Lax New Mathematical Library, and served on the MAA Notes Editorial Board, the Haimo Teaching Award Committee, the Beckenbach Book Prize Committee, the Council on Publications, and the Coordinating Council on Awards. He enjoys the challenge of scaling peaks in the mountains of Colorado.