The fundamental group of sympletic manifolds with Hamiltonian lie group actions
نویسندگان
چکیده
منابع مشابه
The Fundamental Group of Symplectic Manifolds with Hamiltonian Lie Group Actions
Let (M,ω) be a connected, compact symplectic manifold equipped with a Hamiltonian G action, where G is a connected compact Lie group. Let φ be the moment map. In [12], we proved the following result for G = S action: as fundamental groups of topological spaces, π1(M) = π1(Mred), where Mred is the symplectic quotient at any value of the moment map φ, and = denotes “isomorphic to”. In this paper,...
متن کاملThe Fundamental Group of Symplectic Manifolds with Hamiltonian Su(2) or So(3) Actions
Let (M,ω) be a connected, compact symplectic manifold equipped with a Hamiltonian SU(2) or SO(3) action. We prove that, as fundamental groups of topological spaces, π1(M) = π1(Mred), where Mred is the symplectic quotient at any value of the moment map φ.
متن کاملTopological Obstructions to Certain Lie Group Actions on Manifolds
Given a smooth closed S1-manifold M , this article studies the extent to which certain numbers of the form (f∗ (x) · P · C) [M ] are determined by the fixed-point set MS 1 , where f : M → K (π1 (M) , 1) classifies the universal cover of M , x ∈ H∗ (π1 (M) ;Q), P is a polynomial in the Pontrjagin classes of M , and C is in the subalgebra of H∗ (M ;Q) generated by H2 (M ;Q). When MS 1 = ∅, variou...
متن کاملDiffeomorphisms of Manifolds with Finite Fundamental Group
We show that the group 3i{M) of pseudoisotopy classes of diffeomorphisms of a manifold of dimension > 5 and of finite fundamental group is commensurable to an arithmetic group. As a result n0{DiffM) is a group of finite type. Let M be an «-dimensional closed smooth manifold, where n > 5, and let DiffM be the group of diffeomorphisms of M. The space DiffM (it is a topological space with the C°°-...
متن کاملAlgebraic Realization of Manifolds with Group Actions
Let G be a compact Lie group and M a closed smooth G manifold. With some restrictions on G or on the isotropy groups of the action we show that M is algebraically realized, i. e., there exists a non-singular real algebraic G variety which is equivariantly diffeomorphic to M .
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 Symplectic Geometry
سال: 2006
ISSN: 1527-5256,1540-2347
DOI: 10.4310/jsg.2006.v4.n3.a4