Seidel Representation for Symplectic Orbifolds

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.

57 pages. v2: minor updates.v3: 58 pages, typos and mistakes corrected, expositions revised, incorrectly displayed figures fixed

References in corpus (2)

• Kuranishi homology and Kuranishi cohomology
• Canonical models of filtered $A_{\infty }$-algebras and Morse complexes

Cited by in corpus (2)

• Seidel Representations and Quantum Cohomology of Toric Orbifolds
• Seidel elements and mirror transformations for toric stacks