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
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Source Wikipedia: Freedman classification
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Source Wikipedia: Freedman classification
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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
Proved By: Michael Freedman, Lead
Freedman's classification is named after Michael Freedman, who published it in 1982 and who was awarded the Fields Medal for it in 1986.
In Group: Geometric and Differential Topology, Lead paragraph
In topology in mathematics, Freedman's classification (or Freedman's theorem) is a central result about four-dimensional topological manifolds (short 4-manifolds).
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.
Lead section
Freedman's classification is named after Michael Freedman, who published it in 1982 and who was awarded the Fields Medal for it in 1986.
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