Differential and Low-Dimensional Topology

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2023
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
ISBN-13:	9781009220576
ISBN-10:	1009220578
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Juhász, András
Hersteller:	Cambridge University Press
Maße:	229 x 154 x 17 mm
Von/Mit:	András Juhász
Erscheinungsdatum:	20.04.2023
Gewicht:	0,377 kg

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