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Conley Conjecture for Negative Monotone Symplectic Manifolds
Conley Conjecture Negative Monotone Symplectic Manifolds
2010/11/24
We prove the Conley conjecture for negative monotone, closed symplectic manifolds, i.e., the existence of infinitely many periodic orbits for Hamiltonian diffeomorphisms of such manifolds.
Cohomology and Hodge Theory on Symplectic Manifolds: II
Cohomology Hodge Theory Symplectic Manifolds: II
2010/11/11
We show that the exterior derivative operator on a symplectic manifold has a natural decomposition into two linear differential operators, analogous to the Dolbeault operators in complex geometry. The...
Poisson smooth structures on stratified symplectic spaces
Poisson smooth structures stratified symplectic spaces
2010/11/9
In this note we introduce the notion of a Poisson smooth structure on a symplectic stratified space. We show that under a mild condition many properties of a symplectic manifold can be extended to a ...
Mass generation mechanism for spin 1/2 fermions in Dirac--Yang--Mills model equations with a symplectic gauge symmetry
Mass generation mechanism spin 1/2 fermions symplectic gauge symmetry
2010/12/8
n the StandardModel of electroweak interactions the fundamental fermions acquire masses by the Yukawa interaction with the (spin 0) Higgs field. In our model spin 1/2 fermions acquire masses by an int...
We prove the Poisson geometric version of the Local Reeb Stability (from foliation theory) and of the Slice Theorem (from equivariant geometry),which is also a generalization of Conn’s linearization t...
A proof of Wahl's conjecture in the symplectic case
proof of Wahl's conjecture symplectic case
2010/11/29
Let X denote a flag variety of type A or type C. We construct a canonical Frobenius splitting of X ×X which vanishes with maximal multiplicty along the diagonal. This way we verify a conjecture by Lak...
The Standard Conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces
Standard Conjectures holomorphic symplectic varieties deformation Hilbert schemes of K3 surfaces
2010/11/29
We prove the standard conjectures for complex projective varieties that are deformations of the Hilbert scheme of points on a K3 surface. The proof involves Verbitsky’s theory of hyperholomorphic shea...
Transversality theory, cobordisms, and invariants of symplectic quotients
Transversality theory cobordisms invariants symplectic quotients
2010/10/29
This paper gives methods for understanding invariants of symplectic quotients. The symplectic quotients considered here are compact symplectic manifolds (or more generally orbifolds), which arise as t...