We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigid...We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau (Topology, 18, 1979, 361-380). As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of CP2×V, where V is a closed smooth manifold admitting a real analytic Riemannian metric of non-positive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one dimensional cohomology.展开更多
The author proves several embedding theorems for finite covering maps, principal G-bundlesinto bundles. The main results are1. Let π: E→X be a finite covering mapt and X a connected locally pathconnectedparacompact ...The author proves several embedding theorems for finite covering maps, principal G-bundlesinto bundles. The main results are1. Let π: E→X be a finite covering mapt and X a connected locally pathconnectedparacompact space. If cat X≤5 k, then the finite covering space π: E→X can be embeddedinto the trivial real k-plane bundle.2. Let x: E→ X be a principal G-bundle over a paracompact space. If there exists alinear action of G on F (F = R or C) and cat X≤ k, then π: E→X can be embedded intofor any F-vector bundles ζi, i = 1,’’’ k.展开更多
基金Project supported by the Japanese Government Scholarshipthe Japan Society for the Promotion of Science Postdoctoral Fellowship for Foreign Researchers+2 种基金the Focused Research Group Postdoctoral Fellowshipthe Program of Visiting Scholars at Chern Institute of Mathematicsthe National Natural Science Foundation of China (No. 10601053).
文摘We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau (Topology, 18, 1979, 361-380). As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of CP2×V, where V is a closed smooth manifold admitting a real analytic Riemannian metric of non-positive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one dimensional cohomology.
文摘The author proves several embedding theorems for finite covering maps, principal G-bundlesinto bundles. The main results are1. Let π: E→X be a finite covering mapt and X a connected locally pathconnectedparacompact space. If cat X≤5 k, then the finite covering space π: E→X can be embeddedinto the trivial real k-plane bundle.2. Let x: E→ X be a principal G-bundle over a paracompact space. If there exists alinear action of G on F (F = R or C) and cat X≤ k, then π: E→X can be embedded intofor any F-vector bundles ζi, i = 1,’’’ k.
