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# Journal of Noncommutative Geometry

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**Volume 11, Issue 3, 2017, pp. 827–843**

**DOI: 10.4171/JNCG/11-3-2**

Published online: 2017-09-26

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

Safdar Quddus^{[1]}(1) National Institute of Science Education & Research, Jatni, India

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 $K_0 (\mathcal A_θ^\mathrm {alg} \rtimes \mathbb Z_2)$.

*Keywords: *Cyclic cohomology, noncommutative torus, Chern–Connes index

Quddus Safdar: Cohomology of $\mathcal A_θ^\mathrm {alg} \rtimes \mathbb Z_2$ and its Chern–Connes pairing. *J. Noncommut. Geom.* 11 (2017), 827-843. doi: 10.4171/JNCG/11-3-2