### text ↠ Smooth Four Manifolds and Complex Surfaces Ergebnisse der Mathematik und ihrer Grenzgebiete 3 FolgeA Series of Modern Surveys in Mathematics Ñ Robert Friedman

In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or eual to 5 129 and proceeded to prove the h cobordism theorem 130 This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5 By the mid 1970's the main outlines of this theory were complete and explicit answers especially concerning simply connected manifolds as well as general ualitative results had been obtai

### Robert Friedman Ñ Smooth Four Manifolds and Complex Surfaces Ergebnisse der Mathematik und ihrer Grenzgebiete 3 FolgeA Series of Modern Surveys in Mathematics doc

Smooth Four Manifolds and Complex Surfaces Ergebnisse der Mathematik und ihrer Grenzgebiete 3 FolgeA Series of Modern Surveys in MathematicsNed As an example of such a ualitative result a closed simply connected manifold of dimension 2 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes There are similar results for self diffeomorphisms which at least in the simply connected case say that the group of self diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all auto