On the Rozansky-Witten TQFT
This thesis studies a potential method for constructing the Rozansky--Witten TQFT as an extended $(1+1+1)$-TQFT. A monoidal $2$-category consisting of schemes, complexes of sheaves and sheaf morphisms is constructed, and it is shown that there are $(1+1)$-TQFTs valued in the truncation of this categ...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
2020
|
| Subjects: |
| _version_ | 1826290880213942272 |
|---|---|
| author | Banks, P |
| author2 | Juhasz, A |
| author_facet | Juhasz, A Banks, P |
| author_sort | Banks, P |
| collection | OXFORD |
| description | This thesis studies a potential method for constructing the Rozansky--Witten TQFT as an extended $(1+1+1)$-TQFT. A monoidal $2$-category consisting of schemes, complexes of sheaves and sheaf morphisms is constructed, and it is shown that there are $(1+1)$-TQFTs valued in the truncation of this category, whose state spaces agree with the Rozansky--Witten TQFT. However, it is also shown that if such a TQFT is based on a reduced Noetherian scheme, it cannot be extended upwards to a $(1+1+1)$-TQFT. |
| first_indexed | 2024-03-07T02:50:58Z |
| format | Thesis |
| id | oxford-uuid:ada9d356-9832-436a-aaf7-6a2fb663eba0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:50:58Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | oxford-uuid:ada9d356-9832-436a-aaf7-6a2fb663eba02022-03-27T03:37:17ZOn the Rozansky-Witten TQFTThesishttp://purl.org/coar/resource_type/c_db06uuid:ada9d356-9832-436a-aaf7-6a2fb663eba0Algebraic topologyEnglishHyrax Deposit2020Banks, PJuhasz, AThis thesis studies a potential method for constructing the Rozansky--Witten TQFT as an extended $(1+1+1)$-TQFT. A monoidal $2$-category consisting of schemes, complexes of sheaves and sheaf morphisms is constructed, and it is shown that there are $(1+1)$-TQFTs valued in the truncation of this category, whose state spaces agree with the Rozansky--Witten TQFT. However, it is also shown that if such a TQFT is based on a reduced Noetherian scheme, it cannot be extended upwards to a $(1+1+1)$-TQFT. |
| spellingShingle | Algebraic topology Banks, P On the Rozansky-Witten TQFT |
| title | On the Rozansky-Witten TQFT |
| title_full | On the Rozansky-Witten TQFT |
| title_fullStr | On the Rozansky-Witten TQFT |
| title_full_unstemmed | On the Rozansky-Witten TQFT |
| title_short | On the Rozansky-Witten TQFT |
| title_sort | on the rozansky witten tqft |
| topic | Algebraic topology |
| work_keys_str_mv | AT banksp ontherozanskywittentqft |