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Zailai, Mohmmad Accepted Dissertation 3-8-22 Sp 22.pdf (2.11 MB)
ETD Abstract Container
Abstract Header
Topological Field Theories with Defects
Author Info
Zailai, Mohmmad
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1646737048910495
Abstract Details
Year and Degree
2022, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).
Abstract
Topological field theories are important due to their numerous applications in theoretical physics and modern mathematics. A useful way to study topological field theories is by using category theory. In this dissertation we considered different types of topological filed theories in dimension two. R.Dijkraaf found that the category $2\C ob_{c}$ of surfaces is free on a commutative Frobenius algebra. G.Segal and G.Moore showed that the category $2\C ob_{o\da c}$ of open surfaces is described by a Cardy pair. We extended these results to the following: the category $2\C ob_{2o}$ of two coloured ribbon graphs is free on a pair of Frobenius algebras and a Frobenius bimodule. In a separable case, a Frobenius bimodule and its dual form a Morita context. We also found that the category $2\C ob_{2o\da c}$ of two coloured open surfaces is the free monoidal category on a bimodule btween two Cardy pairs. We moved then to the category $2\C ob_{d}$ of surfaces with defect of codimension 1. We gave a dicribtion of Cardy correspondences in this category and ended up with a conjecture stating that the category $2\C ob_{d}$ is free on a Cardy correspondence in a separable case, i.e. all Frobenius algebras are separable. We gave an example of a 2 dimensional topological field theory which we call a set-theoretic 2 dimensional topological field theory. The target of this functor is the category of correspondences $\C orr$. We showed that any Frobenius monoid in $\C orr$ is a multi-fusion ring.
Committee
Alexei Davydov, Professor (Advisor)
Nancy Sandler (Committee Member)
Marcel Bischoff, Professor (Committee Member)
Vladimir Uspenskiy, Professor (Committee Member)
Pages
98 p.
Subject Headings
Mathematics
Keywords
Topological
;
Field Theories
;
Defectsmat
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Citations
Zailai, M. (2022).
Topological Field Theories with Defects
[Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1646737048910495
APA Style (7th edition)
Zailai, Mohmmad.
Topological Field Theories with Defects .
2022. Ohio University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1646737048910495.
MLA Style (8th edition)
Zailai, Mohmmad. "Topological Field Theories with Defects ." Doctoral dissertation, Ohio University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1646737048910495
Chicago Manual of Style (17th edition)
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Document number:
ohiou1646737048910495
Download Count:
126
Copyright Info
© 2022, all rights reserved.
This open access ETD is published by Ohio University and OhioLINK.