# Book:Robert Messer/Topology Now!

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## Robert Messer and Philip Straffin:

## Robert Messer and Philip Straffin: *Topology Now!*

Published $2006$, **Mathematical Association of America**

- ISBN 978-0883857441.

### Subject Matter

### 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**