Abstract
We start with a discussion of the more familiar 3-dimensional Poincare conjecture whose solution constitutes a major achievement of modern geometric analysis. This motivates the precise formulation of the smooth 4 dimensional Poincare conjecture given in this article. Then we explain the difference between the topological and smooth structures on a manifold as well as the groundbreaking work of Donaldson in defining differential invariant for 4-dimensional manifolds using Yang-Mills instanton. At the end, we give some recent approaches in the attack of the conjecture
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