The Disc Embedding Theorem

Behrens, S., Kalmar, B., Kim, M. H., Powell, M. and Ray, A. (Eds.) (2021) The Disc Embedding Theorem. Oxford University Press: Oxford. ISBN 9780198841319

Abstract

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 Poincaré 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.

• Item Type: Edited Books
• Status: Published
• Glasgow Author(s) Enlighten ID: Powell, Dr Mark
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Publisher: Oxford University Press
• ISBN: 9780198841319