We introduce two monoidal supercategories: the odd dotted Temperley-Lieb category TLo,•(δ), which is a generalization of the odd Temperley-Lieb category studied by Brun-dan and Ellis in [5], and the odd annular Bar-Natan category BNo(A), which generalizes the odd Bar-Natan category studied by Putyra in [16]. We then show there is an equivalence of categories between them if δ=0. We use this equivalence to better understand the action of the Lie superalgebra gl(1|1) on the odd Khovanov homology of a knot in a thickened annulus found by Grigsby and Wehrli in [7].
","abstract_html":"<p>We introduce two monoidal supercategories: the odd dotted Temperley-Lieb category TLo,•(δ), which is a generalization of the odd Temperley-Lieb category studied by Brun-dan and Ellis in [5], and the odd annular Bar-Natan category BNo(A), which generalizes the odd Bar-Natan category studied by Putyra in [16]. We then show there is an equivalence of categories between them if δ=0. We use this equivalence to better understand the action of the Lie superalgebra gl(1|1) on the odd Khovanov homology of a knot in a thickened annulus found by Grigsby and Wehrli in [7].</p>","abstract_has_math":false,"creators":["Necheles, Casey"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Wehrli, Stephan","Miller, Claudia"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-07-16T07:00:00Z","date_published":"2021-07-16T07:00:00Z","updated_at":"2026-07-24T04:56:14Z","subjects":["Knot Theory","Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://surface.syr.edu/etd/1345","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Wehrli, Stephan","Miller, Claudia"]},{"key":"dc:creator","label":"Author","values":["Necheles, Casey"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"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":["Knot Theory","Mathematics","Physical Sciences and Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://surface.syr.edu/etd/1345"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We introduce two monoidal supercategories: the odd dotted Temperley-Lieb category TLo,•(δ), which is a generalization of the odd Temperley-Lieb category studied by Brun-dan and Ellis in [5], and the odd annular Bar-Natan category BNo(A), which generalizes the odd Bar-Natan category studied by Putyra in [16]. We then show there is an equivalence of categories between them if δ=0. We use this equivalence to better understand the action of the Lie superalgebra gl(1|1) on the odd Khovanov homology of a knot in a thickened annulus found by Grigsby and Wehrli in [7].
"]},{"key":"dc:title","label":"Title","values":["Odd annular Bar-Natan Category and Gl(1|1)"]}]}],"canonical_facts":{"dc:contributor":["Wehrli, Stephan","Miller, Claudia"],"dc:creator":["Necheles, Casey"],"dc:description.abstract":["We introduce two monoidal supercategories: the odd dotted Temperley-Lieb category TLo,•(δ), which is a generalization of the odd Temperley-Lieb category studied by Brun-dan and Ellis in [5], and the odd annular Bar-Natan category BNo(A), which generalizes the odd Bar-Natan category studied by Putyra in [16]. We then show there is an equivalence of categories between them if δ=0. We use this equivalence to better understand the action of the Lie superalgebra gl(1|1) on the odd Khovanov homology of a knot in a thickened annulus found by Grigsby and Wehrli in [7].
"],"dc:identifier":["https://surface.syr.edu/etd/1345"],"dc:subject":["Knot Theory","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Odd annular Bar-Natan Category and Gl(1|1)"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T04:56:14Z"}