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The Disc Embedding Theorem (Hardcover)
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The Disc Embedding Theorem (Hardcover)
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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 Poincare 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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