Book:Robert Messer/Topology Now!

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