Freedman's Theorem classifies simply connected, compact, four-dimensional topological manifolds up to homeomorphism by a small set of algebraic invariants, chiefly the manifold's intersection form together, in the case of an odd form, with an extra invariant distinguishing two homeomorphism types for the same form. Named for Michael Freedman, who proved it in 1982, it settled the topological, though not the smooth, case of the four-dimensional Poincare Conjecture, showing that a simply connected topological four-manifold with the intersection form of the ordinary four-sphere must be homeomorphic to that sphere.
Facts
StatementEvery symmetric unimodular bilinear form is the intersection form of a simply connected oriented closed topological 4 manifold. 2 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Wikipedia: Freedman classification
Sources
1. Wikipedia: Freedman classification
WikipediaLead section, statement-form reference
Concretely, it gives a full classification of all simply connected oriented closed topological 4-manifolds up to orientation-preserving homeomorphism by their intersection form and their Kirby-Siebenmann invariant.
In Branch: Topology, Lead sentence
In topology in mathematics, Freedman's classification (or Freedman's theorem) is a central result about four-dimensional topologic
View the Source 2. Freedman's theorem (Wikipedia)
Statement section
Every symmetric unimodular bilinear form is the intersection form of a simply connected oriented closed topological 4-manifold.
History section, publication note
published in 1982 in Freedman's paper The topology of four-dimensional manifolds in the Journal of Differential Geometry
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