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 $\mathbb{R}{P}_q^2$ . In this article we calculate the Hochschild and cyclic homology and cohomology groups of these orbifolds and also the corresponding Chern-Connes indices.