Differential and Low-Dimensional Topology
Seiten
2023
Cambridge University Press (Verlag)
978-1-009-22060-6 (ISBN)
Cambridge University Press (Verlag)
978-1-009-22060-6 (ISBN)
This short book for graduate students presents the essential parts of differential and low-dimensional topology so that the reader may become 'literate' in the field and begin research as quickly as possible, while keeping the prerequisites to a minimum. A novel feature at this level is the inclusion of the modern theory of Heegaard Floer homology.
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.
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.
András Juhász is Professor of Mathematics at the University of Oxford. He specialises in low-dimensional topology and knot theory from the point of view of invariants such as Heegaard Floer homology. Recently, in collaboration with DeepMind, he has been exploring how machine learning might be used to advance pure mathematics.
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; Bibliography; Index.
| Erscheinungsdatum | 03.04.2023 |
|---|---|
| Reihe/Serie | London Mathematical Society Student Texts |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 158 x 235 mm |
| Gewicht | 510 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-009-22060-8 / 1009220608 |
| ISBN-13 | 978-1-009-22060-6 / 9781009220606 |
| Zustand | Neuware |
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