Introduction to 3-Manifolds

Contents: Preface. 1. Perspectives on manifolds. 2. Surfaces. 3. 3-manifolds. 4. Knots and links in 3-manifolds. 5. Triangulated 3-manifolds. 6. Heegaard splitting. 7. Further topics. 8. General position. 9. Morse functions. Bibliography. Index.

This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology.

The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex.

With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.