The disc embedding theorem /
The Disc Embedding Theorem contains the first thorough and approachable exposition of Freedman's proof of the disc embedding theorem.
| Other Authors: | , , , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Oxford :
Oxford University Press,
2021.
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| Edition: | First edition. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | The Disc Embedding Theorem contains the first thorough and approachable exposition of Freedman's proof of the disc embedding theorem. The disc embedding theorem provides a detailed proof of the eponymous theorem in 4-manifold topology. The theorem, due to Michael Freedman, underpins virtually all of our understanding of 4-manifolds in the topological category. Most famously, this includes the 4-dimensional topological Poincaré conjecture. Combined with the concurrent work of Simon Donaldson, the theorem reveals a remarkable disparity between the topological and smooth categories for 4-manifolds. A thorough exposition of Freedman's proof of the disc embedding theorem is given, 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. Techniques from decomposition space theory are used to show that an object produced by an infinite, iterative process, which we call a skyscraper, is homeomorphic to a thickened disc, relative to its boundary. A stand-alone interlude explains the disc embedding theorem's key role in smoothing theory, the existence of exotic smooth structures on Euclidean space, and all known homeomorphism classifications of 4-manifolds via surgery theory and the s-cobordism theorem. The book is written to be accessible to graduate students working on 4-manifolds, as well as researchers in related areas. It contains over a hundred professionally rendered figures. |
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| Physical Description: | 1 online resource (xvii, 473 pages) : illustrations (some color). |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9780192578389 0192578383 9780191876929 0191876925 |