Morphisms of its so called rational minimal model which preserve the Pontrjagin classes 131 Once the high dimensional theory was in good shape attention shifted to the remaining and seemingly xceptional dimensions 3 and 4 The theory behind the results manifolds of dimension at least results for manifolds of dimension at does not carryover to manifolds of these low dimensions The Fountains of Paradise essentially because there is no longernough room to maneuver Thus new ideas are necessary to study manifolds of these low dimensio. ,

In 1961 Smale stablished the Conjecture In Dimensions Poincare Conjecture in dimensions than or ual to 5 129 and proceeded the h cobordism theorem 130 This result inaugurated a major ffort 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 xplicit answers specially concerning simply connected manifolds as well as general ualitative results had been obtai. ,

Ned As an xample of Such A Ualitative Result A Closed Simply a ualitative result a closed simply 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. ,

## Robert Friedman ´ 7 characters

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