The Disc Embedding Theorem (eBook, PDF)

Redaktion: Behrens, Stefan; Ray, Arunima; Powell, Mark; Kim, Min Hoon; Kalmar, Boldizsar

• Format: PDF

Produktbeschreibung

Based on Fields medal winning work of Michael Freedman, this book explores the disc embedding theorem for 4-dimensional manifolds. This theorem underpins virtually all our understanding of topological 4-manifolds. Most famously, this includes the 4-dimensional Poincar? conjecture in the topological category. The Disc Embedding Theorem contains the first thorough and approachable exposition of Freedman's proof of the disc embedding theorem, with many new details. A self-contained account of decomposition space theory, a beautiful but outmoded branch of topology that produces non-differentiable homeomorphisms between manifolds, is provided, as well as a stand-alone interlude that explains the disc embedding theorem's key role in all known homeomorphism classifications of 4-manifolds via surgery theory and the s-cobordism theorem. Additionally, the ramifications of the disc embedding theorem within the study of topological 4-manifolds, for example Frank Quinn's development of fundamental tools like transversality are broadly described. The book is written for mathematicians, within the subfield of topology, specifically interested in the study of 4-dimensional spaces, and includes numerous professionally rendered figures.

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Produktdetails

• Verlag: Oxford University Press
• Seitenzahl: 300
• Erscheinungstermin: 15. Juli 2021
• Englisch
• ISBN-13: 9780192578389
• Artikelnr.: 62172891