Smooth Four-Manifolds and Complex Surfaces

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The book delves into the advancements in topology and geometry initiated by Smale's establishment of the generalized Poincare Conjecture in higher dimensions and the h-cobordism theorem. It outlines the classification of smooth and topological structures on manifolds of dimension 5 and above, highlighting significant results regarding simply connected manifolds. As the theory matured, focus shifted to the more complex and unique challenges posed by 3 and 4-dimensional manifolds, necessitating innovative approaches due to the limitations inherent in these lower dimensions.