Sullivan is one of the founders of the surgery method of classifying high-dimensional manifolds, along with Browder, Sergei Novikov and C. T. C. Wall.
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An obstruction to the manifold version was formulated by Andrew Casson and Dennis Sullivan in 1967–9 (originally in the simply-connected case), using the Rochlin invariant and the cohomology group H3(M;Z/2Z).