nLab symplectic orbifold

Idea

A symplectic orbifold is an orbifold with symplectic structure, hence like a symplectic manifold but possibly with singularities modeled on fixed points of local actions of finite groups of symplectomorphisms.

Related concepts

• Riemannian orbifold

• complex orbifold

• Lorentzian orbifold

References

• Leonor Godinho, Blowing Up Symplectic Orbifolds, Annals of Global Analysis and Geometry 20, 117–162 (2001) (doi:10.1023/A:1011628628835)

• Weimin Chen, Resolving symplectic orbifolds with applications to finite group actions, Journal of Gökova Geometry Topology 12 (2018), 1-39 (arXiv:1708.09428)

• Juan Ángel Rojo Carulli, Orbifolds and geometric structures (2019) (eprints.ucm.es/56824/)

On orbifold cohomology of symplectic orbifolds:

• Vasily Dolgushev, Pavel Etingof, Hochschild cohomology of quantized symplectic orbifolds and the Chen-Ruan cohomology, Int. Math. Res. Not. 2005, no. 27, 1657-1688 (arXiv:math/0410562)

• Tara Holm, Tomoo Matsumura, Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds, Transformation Groups 17, 717–746 (2012) (arXiv:1008.3315, doi:10.1007/s00031-012-9192-7)

• Cheol-Hyun Cho, Mainak Poddar, Holomorphic orbi-discs and Lagrangian Floer cohomology of symplectic toric orbifolds, J. Differential Geom. Volume 98, Number 1 (2014), 21-116 (euclid:jdg/1406137695)