Webs and Foams of Simple Lie Algebras- [electronic resource]
Webs and Foams of Simple Lie Algebras- [electronic resource]
- 자료유형
- 학위논문파일 국외
- 최종처리일시
- 20240214101252
- ISBN
- 9798379786878
- DDC
- 510
- 서명/저자
- Webs and Foams of Simple Lie Algebras - [electronic resource]
- 발행사항
- [S.l.]: : Columbia University., 2023
- 발행사항
- Ann Arbor : : ProQuest Dissertations & Theses,, 2023
- 형태사항
- 1 online resource(88 p.)
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
- 주기사항
- Advisor: Khovanov, Mikhail.
- 학위논문주기
- Thesis (Ph.D.)--Columbia University, 2023.
- 사용제한주기
- This item must not be sold to any third party vendors.
- 초록/해제
- 요약In the first part of the dissertation, we construct two-dimensional TQFTs which categorify the evaluations of circles in Kuperberg's \uD835\uDC352 spider. We give a purely combinatorial evaluation formula for these TQFTs and show that it is compatible with the trace map on the corresponding commutative Frobenius algebras. Furthermore, we develop a theory of Θ-foams and their combinatorial evaluations to lift the ungraded evaluation of the \uD835\uDF03-web, thus paving a way for categorifying \uD835\uDC352 webs to \uD835\uDC352 foams. In the second part of the dissertation, we study the calculus of unoriented \uD835\uDD30\uD835\uDD293 webs and foams. We focus on webs with a small number of boundary points. We obtain reducible collections and consider bilinear forms on these collections given by pairings of webs. We give web categories stable under the action of certain endofunctors and derive relations between compositions of these endofunctors.
- 일반주제명
- Mathematics.
- 일반주제명
- Applied mathematics.
- 키워드
- TQFTs
- 키워드
- Calculus
- 키워드
- Bilinear forms
- 키워드
- Endofunctors
- 기타저자
- Columbia University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 85-01B.
- 기본자료저록
- Dissertation Abstract International
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.