Anti-symplectic involutions with lagrangian fixed loci and their quotients
نویسندگان
چکیده
منابع مشابه
A Note on Lagrangian Loci of Quotients
We study hamiltonian actions of compact groups in the presence of compatible involutions. We show that the lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces corresponding to involutions on the group strongly inner to the given one. Our techniques imply that the solution to the eigenvalues of a sum problem for a ...
متن کاملThe Mod 2 Cohomology of Fixed Point Sets of Anti-symplectic Involutions
Let M be a compact, connected symplectic manifold with a Hamiltonian action of a compact n-dimensional torus G = Tn. Suppose that σ is an anti-symplectic involution compatible with the G-action. The real locus of M is X, the fixed point set of σ. Duistermaat uses Morse theory to give a description of the ordinary cohomology of X in terms of the cohomology of M . There is a residual GR = (Z/2Z) ...
متن کاملDiscriminant of Symplectic Involutions
We define an invariant of torsors under adjoint linear algebraic groups of type Cn—equivalently, central simple algebras of degree 2n with symplectic involution—for n divisible by 4 that takes values in H(k, μ2). The invariant is distinct from the few known examples of cohomological invariants of torsors under adjoint groups. We also prove that the invariant detects whether a central simple alg...
متن کاملLagrangian Integration with Symplectic Methods
In this short note we show how to obtain Lagrangian integrators from known sym-plectic partitioned Runge-Kutta methods.
متن کاملClassification of Lagrangian stars and their symplectic reductions
The Lagrangian star is a germ of the system ({L1, . . . , Lk}, p̃) of Lagrangian submanifolds in the symplectic manifold (M,ω). We investigate the symplectic group action on Lagrangian stars and construct the basic invariants of such action. The Kashiwara signature for 3-Lagrangian linear stars is generalized to the nonlinear case and the generalized contact classes for Lagrangian stars are cons...
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: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06391-8