On the nonexistence of certain morphisms from Grassmannian to Grassmannian in characteristic 0.
Let LX be the space of free loops on a simply connected manifold X. When the real cohomology of X is a tensor product of algebras generated by a single element, we determine the algebra structure of the real cohomology of LX by using the cyclic bar complex of the de Rham complex Ω(X) of X. In consequence, the algebra generators of the real cohomology of LX can be represented by differential forms on LX through Chen’s iterated integral map. Let be the circle group. The -equivariant cohomology...
For a typical example of a complete discrete valuation field of type II in the sense of [12], we determine the graded quotients for all . In the Appendix, we describe the Milnor -groups of a certain local ring by using differential modules, which are related to the theory of syntomic cohomology.