Seidel Representation for Symplectic Orbifolds
arXiv:1207.4246
Abstract
Let $(\X,ω)$ be a compact symplectic orbifold. We define $π_1(Ham(\X, ω))$, the fundamental group of the 2-group of Hamiltonian diffeomorphisms of $(\X, ω)$, and construct a group homomorphism from $π_1(Ham(\X, ω))$ to the group $QH_{orb}^*(\X,Λ)^{\times}$ of multiplicatively invertible elements in the orbifold quantum cohomology ring of $(\X, ω)$. This extends the Seidel representation ([Se], [M]) to symplectic orbifolds.
arXiv comment57 pages. v2: minor updates.v3: 58 pages, typos and mistakes corrected, expositions revised, incorrectly displayed figures fixed
References in corpus (9)
- A New Cohomology Theory for Orbifold
- Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
- Cyclic symmetry and adic convergence in LagrangianFloer theory
- Non-Compact Symplectic Toric Manifolds
- Hamiltonian group actions on symplectic Deligne-Mumford stacks and toric orbifolds
- Kuranishi homology and Kuranishi cohomology
- Relative orbifold Gromov-Witten theory and degeneration formula
- Lagrangian Floer theory on compact toric manifolds II : Bulk deformations
- Canonical models of filtered -algebras and Morse complexes