Study of groups of measure-preserving homeomorphisms and volume-preserving diffeomorphisms of noncompact manifolds

研究了非紧流形M的自同态群和同胚群的拓扑性质。在紧开C∞拓扑下，我们将Moser体积形式定理的参数化形式推广到非紧情形.对于Whitney C∞拓扑，我们证明了M的同胚群和具有紧支集的群的子群对局部同胚于l ~ 2的可数箱积和小箱积对.对于一致拓扑，我们还得到了一致嵌入空间和一致同胚群的变形定理.

We studied topological properties of groups of diffeomorphisms and homeomorphisms of any on-compact manifold M. Under the compact-open C∞topology, we extended a parametrized version of Moser’s theorem for volume forms to the non-compact case. As for the Whitney C∞ topology, we howed That the pair of the group of diffeomorphisms of M and the subgroup of those with compact support is Locally homeomorphic to the pair of countable box product and small box product of l2.As for the uniform topology, we also obtained some deformation theorems for spaces of uniform embeddings and Groups of uniform homeomorphisms.