On isomorphic classical diffeomorphism groups. II
نویسندگان
چکیده
منابع مشابه
Homomorphisms between Diffeomorphism Groups
For r ≥ 3, p ≥ 2, we classify all actions of the groups Diffc(R) and Diff+(S) by Cdiffeomorphisms on the line and on the circle. This is the same as describing all nontrivial group homomorphisms between groups of compactly supported diffeomorphisms on 1-manifolds. We show that all such actions have an elementary form, which we call topologically diagonal. As an application, we answer a question...
متن کاملMaximal prehomogeneous subspaces on classical groups
Suppose $G$ is a split connected reductive orthogonal or symplectic group over an infinite field $F,$ $P=MN$ is a maximal parabolic subgroup of $G,$ $frak{n}$ is the Lie algebra of the unipotent radical $N.$ Under the adjoint action of its stabilizer in $M,$ every maximal prehomogeneous subspaces of $frak{n}$ is determined.
متن کاملOn the Uniform Simplicity of Diffeomorphism Groups
We show the uniform simplicity of the identity component Diff(M)0 of the group of Cr diffeomorphisms Diff (Mn) (1 ≤ r ≤ ∞, r = n+1) of the compact connected n-dimensional manifold Mn with handle decomposition without handles of the middle index n/2. More precisely, for any elements f and g of such Diff(M)0 \{id}, f can be written as a product of at most 16n+28 conjugates of g or g−1, which we d...
متن کاملOn the Continuous Cohomology of Diffeomorphism Groups
Suppose that M is a connected orientable n-dimensional manifold and m > 2n. If H(M, R) = 0 for i > 0, it is proved that for each m there is a monomorphism Hm(Wn, O(n)) → H m cont(Diff M, R). If M is closed and oriented, it is proved that for each m there is a monomorphism Hm(Wn, O(n)) → H m−n cont (Diff+ M, R), where Diff+ M is the group of orientation preserving diffeomorphisms of M . 2000 Mat...
متن کاملCurvatures of Sobolev Metrics on Diffeomorphism Groups
Many conservative partial differential equations correspond to geodesic equations on groups of diffeomorphisms. Stability of their solutions can be studied by examining sectional curvature of these groups: negative curvature in all sections implies exponential growth of perturbations and hence suggests instability, while positive curvature suggests stability. In the first part of the paper we s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1988
ISSN: 0022-040X
DOI: 10.4310/jdg/1214442158