This e-book is an exposition of the means of surgical procedure on simply-connected delicate manifolds. Systematic learn of differentiable manifolds utilizing those rules used to be started via Milnor  and Wallace  and built commonly within the final ten years. it truly is now attainable to offer a pretty whole conception of simply-connected manifolds of measurement ~ five utilizing this strategy and that's what i'll try and commence right here. The emphasis has been put on declaring and proving the overall effects essential to practice this technique in numerous contexts. In bankruptcy II, those effects are acknowledged, after which purposes are given to characterizing the homotopy kind of differentiable manifolds and classifying manifolds inside a given homotopy kind. This idea was once first commonly built in Kervaire and Milnor  with regards to homotopy spheres, globalized by way of S. P. Novikov  and the writer  for closed 1-connected manifolds, and prolonged to the bounded case through Wall  and Golo . The thesis of Sullivan  reformed the speculation in a sublime means by way of classifying areas.
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