Cobordism categories and geometric topology (B09)

这个项目涉及流形自同构空间、流形的嵌入空间和流形上的几何结构空间。所使用的方法是几何或同伦理论。特别重要的是配边范畴方法，参数化手术理论，运算理论和函子演算。主要专题：欧几里得空间同胚群的有理同伦性质;一个欧几里得空间到另一个欧几里得空间的拓扑嵌入空间的同伦类型;流形上黎曼度量空间的同伦性质服从曲率条件，如正里奇曲率。

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.