News & Events

Seminar

Date/Time: 
Friday, November 21, 2014 -
15:30 to 16:30
Venue: 
LH-104
Speaker: 
Dr. Safdar Quddus
Title: 
NONCOMMUTATIVE TOROIDAL $SL(2, \mathbb{Z})$ ORBIFOLD
Abstract: The noncommutative torus was introduced in the early 80’s to study a generalization of the classical torus. Connes calculated its cyclic and Hochschild cohomology, his results resembles with the various topological cohomology groups of the classical torus. It is natural to extend these properties to the non-commutative orbifolds. Firstly we talk about motivations behind all these considerations. We then analyse the noncommutative torus orbifold generated by action of finite subgroups of $SL(2, \mathbb{Z})$. Later, we outline the Hochschild and cyclic homology groups of $\mathcal{A}^{alg}_{\theta} \rtimes \Gamma$ for all finite subgroups $\Gamma \subset SL(2, \mathbb{Z})$. We also calculate the cohomology groups of $\mathcal{A}^{alg}_{\theta} \rtimes \mathbb{Z}_2$ and the Chern-Connes pairing as a generalization to the index theory in classical differential geoemtry.

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