Invariants of the $\mathbb{Z}_2$ orbifolds of the Podleś two spheres

Abstract

There are two $\mathbb Z\_2$ orbifolds of the Podleś quantum two-sphere, one being the quantum two-disc $D\_q$ and other the quantum two-dimensional real projective space $\mathbb RP^2\_q$. In this article we calculate the Hochschild and cyclic homology and cohomology groups of these orbifolds and also the corresponding Chern–Connes indices.