Author's School

Graduate School of Arts & Sciences

Author's Department/Program

Mathematics

Language

English (en)

Date of Award

Spring 4-24-2013

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Chair and Committee

Xiang Tang

Abstract

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.

DOI

https://doi.org/10.7936/K7FJ2DVQ

Comments

Permanent URL: http://dx.doi.org/10.7936/K7FJ2DVQ

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Mathematics Commons

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