Cobordism categories and geometric topology (B09)

本课题主要研究流形上的自同构空间、流形上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理论或同伦理论。尤其重要的是协边范畴方法、参数化外科理论、算子理论和函数式演算。主要主题：欧氏空间同胚群的有理同伦性质；一个欧氏空间到另一个欧氏空间的拓扑嵌入的同伦型空间；流形上满足曲率条件的黎曼度量空间的同伦性质，如正Ricci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.