Open Topological Field Theories and 2-Segal Objects
Open Topological Field Theories and 2-Segal Objects
dc.contributor.advisor | Dyckerhoff, Tobias | |
dc.contributor.author | Stern, Walker H. | |
dc.date.accessioned | 2020-04-26T23:23:48Z | |
dc.date.available | 2020-04-26T23:23:48Z | |
dc.date.issued | 17.10.2019 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/8081 | |
dc.description.abstract | In this thesis we analyze 2-dimensional open topological field theories in both 1-categorical and ∞-categorical contexts. Making use of the formalism, introduced by Dyckerhoff and Kapranov, of graphs structured over a crossed simplicial group ∆G, we give combinatorial models for 2-dimensional open cobordism categories with additional structure — orientations, N-spin structures, etc. We then use this model to effect a classification of the corresponding classes of 1-categorical topological field theories. This classification retrieves, in special cases, a number of results known in the literature, as well as providing new results. We then turn to 2-dimensional open oriented topological field theories valued in an ∞-category Span(C) of spans in an ∞-category C. Applying a theorem stated by Lurie in [33], such topological field theories are classified by Calabi-Yau algebras in Span(C). We define two 1-categories whose functors to C parameterize, respectively, associative algebras and Calabi-Yau algebras in Span(C). We prove that there is an equivalence of ∞-categories between associative algebras in Span(C) and 2-Segal simplicial objects in C; and we prove an equivalence of ∞-categories between Calabi-Yau algebras in Span(C) and 2-Segal cyclic objects in C. We discuss the invariants the resultant topological field theories assign to surfaces, and develop the example provided by cyclic structures on Čech nerves. | |
dc.language.iso | eng | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | Topologische Feldtheorie | |
dc.subject | Kategorientheorie | |
dc.subject | ∞-Kategorien | |
dc.subject | Calabi-Yau Algebra | |
dc.subject | Mathematik | |
dc.subject.ddc | 510 Mathematik | |
dc.title | Open Topological Field Theories and 2-Segal Objects | |
dc.type | Dissertation oder Habilitation | |
dc.publisher.name | Universitäts- und Landesbibliothek Bonn | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.identifier.urn | https://nbn-resolving.org/urn:nbn:de:hbz:5n-55917 | |
ulbbn.pubtype | Erstveröffentlichung | |
ulbbnediss.affiliation.name | Rheinische Friedrich-Wilhelms-Universität Bonn | |
ulbbnediss.affiliation.location | Bonn | |
ulbbnediss.thesis.level | Dissertation | |
ulbbnediss.dissID | 5591 | |
ulbbnediss.date.accepted | 27.09.2019 | |
ulbbnediss.institute | Mathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut | |
ulbbnediss.fakultaet | Mathematisch-Naturwissenschaftliche Fakultät | |
dc.contributor.coReferee | Stroppel, Catharina |
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