Introduction to 3-Manifolds

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 specialised 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.

“…Schultens has written an excellent book that richly illustrates the scope of her chosen subject. It is very well written, clear and explicit in its presentation. There are plenty of exercises, and the book has been laboratory tested, so to speak, since it grew out of Schulten’s graduate course on 3-manifolds at Emory University … it will also serve very well indeed as a source for self-study.”-- MAA

Jennifer Schultens, University of California, Davis, CA.