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Abstract Header
On Integrality of SO(n)-Level 2 TQFTs
Author Info
Wang, Yilong
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1525703476442228
Abstract Details
Year and Degree
2018, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
In this thesis, we study properties of the TQFT associated to the modular category SO(p)-level 2 for an odd prime p. We compute the associated representation of the central extension of the mapping class group of the surface of genus one with one boundary component specialized at a simple object a of SO(p)-level 2. Let ζ be a primitive p-th root of unity. We show that for each a, there exists a full-rank free lattice over the ring of integers Z[ζ, i] inside the genus 1 specialized space at a that is preserved by the extended mapping class group action. We also show that for each a, the image of the extended mapping class group representation is finite. Finally, we relate the representations to the Weil representation over finite fields.
Committee
Thomas Kerler (Advisor)
James Cogdell (Committee Member)
David Penneys (Committee Member)
Pages
157 p.
Subject Headings
Mathematics
Keywords
Modular Categories
;
TQFT
;
Integrality
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Citations
Wang, Y. (2018).
On Integrality of SO(n)-Level 2 TQFTs
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1525703476442228
APA Style (7th edition)
Wang, Yilong.
On Integrality of SO(n)-Level 2 TQFTs.
2018. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1525703476442228.
MLA Style (8th edition)
Wang, Yilong. "On Integrality of SO(n)-Level 2 TQFTs." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1525703476442228
Chicago Manual of Style (17th edition)
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Document number:
osu1525703476442228
Download Count:
220
Copyright Info
© 2018, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.