Hamiltonian Gromov –
نویسنده
چکیده
In this paper we introduce invariants of semi-free Hamiltonian actions of S 1 on compact symplectic manifolds (which satisfy some technical conditions related to positivity) using the space of solutions to certain gauge theoretical equations. These equations generalize at the same time the vortex equations and the holomor-phicity equation used in Gromov–Witten theory. In the definition of the invariants we combine ideas coming from gauge theory and the ideas underlying the construction of Gromov–Witten invariants.
منابع مشابه
Gromov–Witten invariants of symplectic quotients and adiabatic limits
We study pseudoholomorphic curves in symplectic quotients as adiabatic limits of solutions to the symplectic vortex equations. Our main theorem asserts that the genus zero invariants of Hamiltonian group actions defined by these equations are related to the genus zero Gromov–Witten invariants of the symplectic quotient (in the monotone case) via a natural ring homomorphism from the equivariant ...
متن کاملImplicit and explicit representations of continuous-time port-Hamiltonian systems
Implicit and explicit representations of smooth, finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations. Explicit representations are derived when ...
متن کاملHamiltonian S1-manifolds Are Uniruled
The main result of this note is that every closed Hamiltonian S manifold is uniruled, i.e. it has a nonzero Gromov–Witten invariant one of whose constraints is a point. The proof uses the Seidel representation of π1 of the Hamiltonian group in the small quantum homology of M as well as the blow up technique recently introduced by Hu, Li and Ruan. It applies more generally to manifolds that have...
متن کاملQuantum homology of fibrations over S
This paper studies the (small) quantum homology and cohomology of fibrations p : P → S whose structural group is the group of Hamiltonian symplectomorphisms of the fiber (M,ω). It gives a proof that the rational cohomology splits additively as the vector space tensor product H(M)⊗H(S), and investigates conditions under which the ring structure also splits, thus generalizing work of Lalonde–McDu...
متن کاملA topological gauged sigma-model
We describe a topological field theory that studies the moduli space of solutions of the symplectic vortex equations. It contains as special cases the topological sigmamodel and topological Yang-Mills over Kähler surfaces. The correlation functions of the theory are closely related to the recently introduced Hamiltonian Gromov-Witten invariants. e-mail address: [email protected] addr...
متن کامل