Book:Robert Messer/Topology Now!

Robert Messer and Philip Straffin: Topology Now!

Published $\text {2006}$, Mathematical Association of America

ISBN 978-0883857441

Subject Matter

• Topology

Contents

Preface

1 Deformations

1.1 Equivalence

1.2 Bijections

1.3 Continuous Functions

1.4 Topological Equivalence

1.5 Topological Invariants

1.6 Isotopy

References and Suggested Readings for Chapter 1

2 Knots and Links

2.1 Knots, Links, and Equivalences

2.2 Knot Diagrams

2.3 Reidemeister Moves

2.4 Colorings

2.5 The Alexander Polynomial

2.6 Skein Relations

2.7 The Jones Polynomial

References and Suggested Readings for Chapter 2

3 Surfaces

3.1 Definitions and Examples

3.2 Cut-and-Paste Techniques

3.3 The Euler Characteristic and Orientability

3.4 Classification of Surfaces

3.5 Surfaces Bounded by Knots

References and Suggested Readings for Chapter 3

4 Three-dimensional Manifolds

4.1 Definitions and Examples

4.2 Euler Characteristic

4.3 Gluing Polyhedral Solids

4.4 Heegaard Splittings

References and Suggested Readings for Chapter 4

5 Fixed Points

5.1 Continuous Functions on Closed Bounded Intervals

5.2 Contraction Mapping Theorem

5.3 Sperner's Lemma

5.4 Brouwer Fixed-Point Theorem for a Disk

References and Suggested Readings for Chapter 5

6 The Fundamental Group

6.1 Deformations with Singularities

6.2 Algebraic Properties

6.3 Invariance of the Fundamental Group

6.4 The Sphere and the Circle

6.5 Words and Relations

6.6 The Poincaré Conjecture

References and Suggested Readings for Chapter 6

7 Metric and Topological Spaces

7.1 Metric Spaces

7.2 Topological Spaces

7.3 Connectedness

7.4 Compactness

7.5 Quotient Spaces

References and Suggested Readings for Chapter 7

Index