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.
","abstract_html":"<p>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 <em>S L</em>(2,) on a noncommutative torus algebra.</p> <p>In the first part, we calculate the Hochschild and cyclic homology of Γ for all finite subgroups Γ <em>S</em> L(2,). In the second part we analyse the cohomology of these algebras and compute the Chern-Connes pairing between the elements of <strong> </strong> and explicit cocycles discovered in our calculations. In the third part we discuss some partial results and conjectures about the corresponding smooth orbifolds.</p>","abstract_has_math":false,"creators":["Quddus, Safdar"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Xiang Tang"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-04-24T07:00:00Z","date_published":"2013-04-24T07:00:00Z","updated_at":"2026-07-24T06:13:14Z","subjects":["Mathematics"],"languages":["English (en)"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7FJ2DVQ"],"render_values":[{"text":"https://doi.org/10.7936/K7FJ2DVQ","href":"https://doi.org/10.7936/K7FJ2DVQ","code":true}]}]},"links":{"outbound_url":"https://openscholarship.wustl.edu/etd/1093","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Xiang Tang"]},{"key":"dc:creator","label":"Author","values":["Quddus, Safdar"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-08-19T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/etd/1093"]},{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7FJ2DVQ"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["On the (Co)Homology of Non-Commutative Toroidal Orbifold"]}]}],"canonical_facts":{"dc:contributor":["Xiang Tang"],"dc:creator":["Quddus, Safdar"],"dc:date.available":["2013-08-19T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://openscholarship.wustl.edu/etd/1093"],"dc:identifier.doi":["https://doi.org/10.7936/K7FJ2DVQ"],"dc:language":["English (en)"],"dc:subject":["Mathematics"],"dc:title":["On the (Co)Homology of Non-Commutative Toroidal Orbifold"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T06:13:14Z"}