Differential and Low-Dimensional Topology

This book provides a concise and accessible introduction to differential and low-dimensional topology for students with an undergraduate background in algebraic topology. It covers essential topics such as exotic seven-spheres, dimension three and knot theory, Heegaard Floer homology, and four-manifold theory, making it an exhilarating and authoritative guide to the field.

Format: Paperback / softback
Length: 229 pages
Publication date: 20 April 2023
Publisher: Cambridge University Press

A newcomer to differential and low-dimensional topology is greeted with a bewildering array of tools and loosely connected theories. This concise book provides a comprehensive overview of the essential elements in each field, enabling readers to gain a solid foundation and embark on research expeditions swiftly. The sole assumption is a foundational course in undergraduate algebraic topology. The first half delves into fundamental concepts of differential topology, culminating in the classification of exotic seven-spheres. It then transitions to dimension three and explores knot theory. Subsequently, an introduction to Heegaard Floer homology, a powerful set of modern invariants for three- and four-manifolds, including knots, emerges in this introductory textbook. The book concludes with a brief glimpse into four-manifold theory. Students will find it an exhilarating and authoritative guide to a vast expanse of the most significant topics in contemporary topology.

Weight: 370g
Dimension: 228 x 151 x 15 (mm)
ISBN-13: 9781009220576