J -holomorphic curves, moment maps, and invariants of Hamiltonian group actions
نویسندگان
چکیده
3 Invariants of Hamiltonian group actions 17 3.1 An action functional . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Symplectic reduction . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Hamiltonian perturbations . . . . . . . . . . . . . . . . . . . . 24 3.4 Moduli spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.5 Fredholm theory . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.6 Compactness . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.7 Invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.8 Adiabatic limits . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.9 Wall crossing and localization . . . . . . . . . . . . . . . . . . 35
منابع مشابه
Se p 19 99 J - holomorphic curves , moment maps , and invariants of Hamiltonian group actions
3 Invariants of Hamiltonian group actions 17 3.1 An action functional . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Symplectic reduction . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Hamiltonian perturbations . . . . . . . . . . . . . . . . . . . . 24 3.4 Moduli spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.5 Fredholm theory . . . . . . . . . . . . . . . . . . ...
متن کاملK-theoretic Invariants for Floer Homology
This paper defines two K-theoretic invariants, Wh1 and Wh2, for individual and one-parameter families of Floer chain complexes. The chain complexes are generated by intersection points of two Lagrangian submanifolds of a symplectic manifold, and the boundary maps are determined by holomorphic curves connecting pairs of intersection points. The paper proves that Wh1 and Wh2 do not depend on the ...
متن کاملComplete Invariants for Hamiltonian Torus Actions with Two Dimensional Quotients
We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces.
متن کاملTall Complexity One Hamiltonian Torus Actions
We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces.
متن کاملPart 2: Pseudo-holomorphic Curves
1. Properties of J-holomorphic curves 1 1.1. Basic definitions 1 1.2. Unique continuation and critical points 5 1.3. Simple curves 8 1.4. Adjunction inequality 9 2. Gromov compactness 12 2.1. Gromov compactness theorem 12 2.2. Energy estimate and bubbling 15 2.3. The isoperimetric inequality 19 2.4. Bubbles connect 22 3. Moduli spaces of J-holomorphic curves 25 3.1. The Fredholm setup 25 3.2. T...
متن کامل