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.
Jennifer Schultens, University of California, Davis, Davis, CA
• Preface 10 • Perspectives on manifolds 12 • Surfaces 40 • 3-manifolds 66 • Knots and links in 3-manifolds 112 • Triangulated 3-manifolds 154 • Heegaard splittings 186 • Further topics 226 • General position 272 • Morse functions 280 • Bibliography 286 • Index 294