Cobordism categories and geometric topology (B09)

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This project is concerned with spaces of manifold automorphisms, spaces of embeddings of manifolds and spaces of geometric structures on manifolds. The methods to be used are geometric or homotopy theoretic. Particularly important are cobordism category methods, parametrized surgery theory, theory of operads and functor calculus. Major themes: rational homotopy properties of homeomorphism groups of Euclidean spaces; homotopy type of spaces of topological embeddings of one euclidean space into another; homotopical properties of spaces of Riemannian metrics on a manifold subject to curvature conditions, such as positive Ricci curvature.