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Math 692: Surgery Theory, Spring 2021

The aim of this course is to introduce the Surgery Theory, which leads to classification of simply-connected manifolds of dimension 5 and above. It enables us to determine whether one can find a manifold within a prescribed homotopy type, and if so, how many such manifolds can be found.

We will begin with basics on manifolds, Morse theory and Smale's h-cobordism theorem. The final goal is to prove several fundamental results due to Novikov, Browder and Sullivan. If time permits, we'll consider also recent developments and applications.

It is required for every student to give a presentation on one of the crucial results of Surgery Theory.