Author's School

Graduate School of Arts & Sciences

Author's Department/Program



English (en)

Date of Award

Spring 4-24-2013

Degree Type


Degree Name

Doctor of Philosophy (PhD)

Chair and Committee

Xiang Tang


Noncommutative torus algebra 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 S L(2,) on a noncommutative torus algebra.

In the first part, we calculate the Hochschild and cyclic homology of Γ for all finite subgroups Γ S L(2,). In the second part we analyse the cohomology of these algebras and compute the Chern-Connes pairing between the elements of and explicit cocycles discovered in our calculations. In the third part we discuss some partial results and conjectures about the corresponding smooth orbifolds.


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