Description
Orient Blackswan Pvt. Ltd. Introduction To 3-Manifolds by JENNIFER SCHULTENS
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.
Table of Contents:- • 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