Differential Topology - Couverture souple

Quick, Gereon

Couverture souple

ISBN 10 : 1009733869 ISBN 13 : 9781009733861

Editeur : Cambridge University Press, 2026

Synopsis

Differential topology uncovers the hidden structure of smooth spaces –the foundation of modern geometry and topology. This book offers a clear, rigorous introduction to the subject, blending theory with concrete examples and applications. Beginning with the basics of manifolds and smooth maps, it develops essential tools and concepts such as tangent spaces, transversality, cobordism, and tubular neighbourhoods, before progressing to powerful invariants like the Brouwer degree, intersection numbers, and the Hopf invariant. Along the way, readers encounter landmark results including Whitney's embedding theorem, Brouwer's fixed point theorem, the Pontryagin construction, Hopf's degree theorem, and the Poincaré–Hopf index theorem. Each chapter combines intuitive explanations with precise and detailed proofs, supported by exercises and detailed solutions that deepen understanding. Ideal for advanced undergraduates, graduate students, and researchers, this text provides a gateway to one of mathematics' most elegant and influential fields – where analysis, geometry, and topology meet.

A propos du livre

À propos de l'auteur

Gereon Quick is Professor of Mathematics at NTNU. His research explores homotopy theory across algebra, geometry, and number theory. He studied and held academic appointments in Cambridge, Paris, Münster, Princeton, and Harvard. His work has been supported by research grants from Germany, Norway, and the USA.

Détails de l'édition

• Éditeur: Cambridge University Press
• Date d'édition: 2026
• Langue: anglais
• ISBN 10: 1009733869
• ISBN 13: 9781009733861
• Reliure: Broché
• Nombre de pages: 400
• Coordonnées du fabricant: Cambridge University Press; https://www.cambridge.org/; ; Via Honduras,15; Pomezia; Italia; 71; Italie