# Cohomology of $\mathcal A_θ^\mathrm {alg} \rtimes \mathbb Z_2$ and its Chern–Connes pairing

### Safdar Quddus

National Institute of Science Education & Research, Jatni, India

## Abstract

We calculate the Hochschild and cyclic cohomology of the noncommutative $\mathbb Z_2$ toroidal algebraic orbifold $\mathcal A_θ^\mathrm {alg} \rtimes \mathbb Z_2$. We also calculate the Chern–Connes pairing of the even periodic cyclic cocycles with the known elements of $K_0 (\mathcal A_θ^\mathrm {alg} \rtimes \mathbb Z_2)$.

## Cite this article

Safdar Quddus, Cohomology of $\mathcal A_θ^\mathrm {alg} \rtimes \mathbb Z_2$ and its Chern–Connes pairing. J. Noncommut. Geom. 11 (2017), no. 3, pp. 827–843

DOI 10.4171/JNCG/11-3-2