{"id":{"repo_id":"ksu","oai_identifier":"oai:krex.k-state.edu:2097/44932"},"canonical_url":"https://search.dev.ndltd.org/etd/ksu/oai:krex.k-state.edu:2097/44932","repository":{"repo_id":"ksu","name":"Kansas State University","base_url":"https://krex.k-state.edu/server/oai/request"},"display":{"title":"A Künneth theorem for the cyclic homology of A-infinity algebras","abstract":"The cyclic homology of a Z/2Z-graded, smooth and proper A-infinity category satisfying the Hodge-to-de-Rham degeneration property carries the structure of a polarized semi-infinite Hodge structure or the so-called EP-structure. Given two A-infinity algebras A and B with the above conditions, we construct a Künneth map from the tensor product of their cyclic homologies to the cyclic homology of the A-infinity tensor product A [circled times] B and show that it respects the EP-structures. As an application, we show that if A and B are equipped with weak Calabi-Yau structures, then A [circled times] B also inherits a weak Calabi-Yau structure. Also, we show that the Künneth quasi-isomorphism respects good splittings of the Hodge filtration on A and B compatible with the weak Calabi-Yau structure. Our explicit calculations rely on the combinatorial (tree) description of the tensor product of A-infinity algebras.","abstract_html":"The cyclic homology of a Z/2Z-graded, smooth and proper A-infinity category satisfying the Hodge-to-de-Rham degeneration property carries the structure of a polarized semi-infinite Hodge structure or the so-called EP-structure. Given two A-infinity algebras A and B with the above conditions, we construct a Künneth map from the tensor product of their cyclic homologies to the cyclic homology of the A-infinity tensor product A [circled times] B and show that it respects the EP-structures. As an application, we show that if A and B are equipped with weak Calabi-Yau structures, then A [circled times] B also inherits a weak Calabi-Yau structure. Also, we show that the Künneth quasi-isomorphism respects good splittings of the Hodge filtration on A and B compatible with the weak Calabi-Yau structure. Our explicit calculations rely on the combinatorial (tree) description of the tensor product of A-infinity algebras.","abstract_has_math":false,"creators":["Azubuike, Henry Chukwunyere"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025","date_published":"2025","updated_at":"2026-07-27T20:01:22Z","subjects":["A-infinity algebra","Hochschild homology","Shuffle product","Calabi-Yau structure"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2097/44932","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Azubuike, Henry Chukwunyere"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-04-15T21:12:10Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-04-15T21:12:10Z"]},{"key":"dc:date.issued","label":"Date","values":["2025"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["A-infinity algebra","Hochschild homology","Shuffle product","Calabi-Yau structure"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/2097/44932"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The cyclic homology of a Z/2Z-graded, smooth and proper A-infinity category satisfying the Hodge-to-de-Rham degeneration property carries the structure of a polarized semi-infinite Hodge structure or the so-called EP-structure. Given two A-infinity algebras A and B with the above conditions, we construct a Künneth map from the tensor product of their cyclic homologies to the cyclic homology of the A-infinity tensor product A [circled times] B and show that it respects the EP-structures. As an application, we show that if A and B are equipped with weak Calabi-Yau structures, then A [circled times] B also inherits a weak Calabi-Yau structure. Also, we show that the Künneth quasi-isomorphism respects good splittings of the Hodge filtration on A and B compatible with the weak Calabi-Yau structure. Our explicit calculations rely on the combinatorial (tree) description of the tensor product of A-infinity algebras."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy"]},{"key":"dc:title","label":"Title","values":["A Künneth theorem for the cyclic homology of A-infinity algebras"]}]}],"canonical_facts":{"dc:creator":["Azubuike, Henry Chukwunyere"],"dc:date.accessioned":["2025-04-15T21:12:10Z"],"dc:date.available":["2025-04-15T21:12:10Z"],"dc:date.issued":["2025"],"dc:description.abstract":["The cyclic homology of a Z/2Z-graded, smooth and proper A-infinity category satisfying the Hodge-to-de-Rham degeneration property carries the structure of a polarized semi-infinite Hodge structure or the so-called EP-structure. Given two A-infinity algebras A and B with the above conditions, we construct a Künneth map from the tensor product of their cyclic homologies to the cyclic homology of the A-infinity tensor product A [circled times] B and show that it respects the EP-structures. As an application, we show that if A and B are equipped with weak Calabi-Yau structures, then A [circled times] B also inherits a weak Calabi-Yau structure. Also, we show that the Künneth quasi-isomorphism respects good splittings of the Hodge filtration on A and B compatible with the weak Calabi-Yau structure. Our explicit calculations rely on the combinatorial (tree) description of the tensor product of A-infinity algebras."],"dc:description.degree":["Doctor of Philosophy"],"dc:identifier.uri":["https://hdl.handle.net/2097/44932"],"dc:subject":["A-infinity algebra","Hochschild homology","Shuffle product","Calabi-Yau structure"],"dc:title":["A Künneth theorem for the cyclic homology of A-infinity algebras"],"dc:type":["Dissertation"]},"updated_at":"2026-07-27T20:01:22Z"}