Orbifold cup products and ring structures on Hochschild cohomologies
K-Theory and Homology
2022-11-11 v1 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
In this paper we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study the relation between this product and an -equivariant version of the Chen--Ruan product. In particular, we give a de Rham model for this equivariant orbifold cohomology.
Keywords
Cite
@article{arxiv.0706.0027,
title = {Orbifold cup products and ring structures on Hochschild cohomologies},
author = {M. J. Pflaum and H. B. Posthuma and X. Tang and H. -H. Tseng},
journal= {arXiv preprint arXiv:0706.0027},
year = {2022}
}