
The Disc Embedding Theorem
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Content
- Preface
- 1: Context for the disc embedding theorem
- 2: Outline of the upcoming proof
- Part 1: Decomposition space theory
- 3: The Schoenflies theorem after Mazur, Morse, and Brown
- 4: Decomposition space theory and the Bing shrinking criterion
- 5: The Alexander gored ball and the Bing decomposition
- 6: A decomposition that does not shrink
- 7: The Whitehead decomposition
- 8: Mixed Bing-Whitehead decompositions
- 9: Shrinking starlike sets
- 10: The ball to ball theorem
- Part II: Building skyscrapers
- 11: Intersection numbers and the statement of the disc embedding theorem
- 12: Gropes, towers, and skyscrapers
- 13: Picture camp
- 14: Architecture of infinite towers and skyscrapers
- 15: Basic geometric constructions
- 16: From immersed discs to capped gropes
- 17: Grope height raising and 1-storey capped towers
- 18: Tower height raising and embedding
- Part III: Interlude
- 19: Good groups
- 20: The s-cobordism theorem, the sphere embedding theorem, and the Poincaré conjecture
- 21: The development of topological 4-manifold theory
- 22: Surgery theory and the classification of closed, simply connected 4-manifolds
- 23: Open problems
- Part IV: Skyscrapers are standard
- 24: Replicable rooms and boundary shrinkable skyscrapers
- 25: The collar adding lemma
- 26: Key facts about skyscrapers and decomposition space theory
- 27: Skyscrapers are standard: an overview
- 28: Skyscrapers are standard: the details
- Bibliography
- Afterword
- Index
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