April 22, 2013 -
9:00 am - 11:00 pm
Location: Danforth University Center, Room 217 |
Host: Prof. Xiang Tang
Abstract: The noncommutative torus was studied in the early 80's as a fundamental example of noncommutative geometry. Connes calculated its cyclic and Hochschild cohomology. In this thesis, we study noncommutative toroidal orbifolds generated by actions of finite subgroups of $ SL (2,\mathbb Z) $ on a noncommutative torus. In the first part, we calculate the Hochschild and cyclic homology of $\mathcal A_\theta^{alg} \rtimes \Gamma $ for all finite subgroups $\Gamma \subset SL (2,\mathbb Z)$. In the second part, we analyze the cohomology of these algebras and compute the pairing of $K_0$-elements of $\mathcal A_\theta^{alg}\rtimes \mathbb{Z}_2$ with explicit cyclic cocycles as a generalization of index theory. We will end with discussing some partial results and conjectures about the corresponding smooth orbifolds.
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