Orbifold Hamiltonian Floer theory for global quotients

TL;DR

This paper develops a new orbifold Hamiltonian Floer theory for global quotient orbifolds, using moduli spaces of holomorphic curves and derived orbifolds to define an ordered flow category.

Contribution

It introduces a bulk-deformed orbifold Floer theory for global quotients, constructing global charts from moduli spaces of holomorphic curves in quotient projective spaces.

Findings

Constructs an orbifold Floer theory for global quotients.

Defines an ordered marked flow category with derived orbifold structures.

Provides a framework for studying symplectic invariants of orbifolds.

Abstract

We construct bulk-deformed orbifold Hamiltonian Floer theory for a global quotient orbifold, that is the quotient of a smooth closed symplectic manifold by a finite group acting faithfully via symplectomorphisms. The moduli spaces define an `ordered marked Flow category', which we equip with a coherent presentation via derived orbifolds. The global charts for orbifold Floer cylinders are built from moduli spaces of holomorphic curves in a quotient of projective space by a free action of the given finite group.