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Differential and Low-Dimensional Topology

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The new student in differential and low-dimensional topology is faced with a bewildering array of tools and loosely connected theories. This short book presents the essential parts of each, enabling the reader to become 'literate' in the field and begin research as quickly as possible. The only prerequisite assumed is an undergraduate algebraic topology course. The first half of the text reviews basic notions of differential topology and culminates with the classification of exotic seven-spheres. It then dives into dimension three and knot theory. There then follows an introduction to Heegaard Floer homology, a powerful collection of modern invariants of three- and four-manifolds, and of knots, that has not before appeared in an introductory textbook. The book concludes with a glimpse of four-manifold theory. Students will find it an exhilarating and authoritative guide to a broad swathe of the most important topics in modern topology.

Author(s): András Juhász
Series: London Mathematical Society Student Texts, 104
Publisher: Cambridge University Press
Year: 2023

Language: English
Pages: 229

Contents
Preface
1 - Background on Topological and Smooth Manifolds
2 - Higher-Dimensional Manifolds
3 - Three-Manifolds
4 - Knots and Links
5 - Heegaard Floer Homology
6 - Four-Manifolds
Appendix - Fibre Bundles and Characteristic Classes
References
Index