Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Solutions to the conjugacy search and decision problems in the braid group using finite conjugacy class invariants
For two braids, A, B ∈ Bn, the conjugacy decision problem asks whether another braid X ∈ Bn exists such that X−1 A X = B. If we know A, B ∈ Bn are indeed conjugate, the conjugacy search problem asks us to find a braid Y ∈ Bn such that Y −1 A Y = B. In this dissertation we investigate a number of sol...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Mathematics and Applied Mathematics
2023
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613252924473344 |
|---|---|
| access_status_str | Open Access |
| author | Erasmus, Sane´ |
| author2 | Blackman, Claire |
| author_browse | Blackman, Claire Erasmus, Sane´ |
| author_facet | Blackman, Claire Erasmus, Sane´ |
| author_sort | Erasmus, Sane´ |
| collection | Thesis |
| description | For two braids, A, B ∈ Bn, the conjugacy decision problem asks whether another braid X ∈ Bn exists such that X−1 A X = B. If we know A, B ∈ Bn are indeed conjugate, the conjugacy search problem asks us to find a braid Y ∈ Bn such that Y −1 A Y = B. In this dissertation we investigate a number of solutions to the conjugacy search problem and conjugacy decision problem in the braid group, all of which use finite invariant subsets of the conjugacy class. In particular, we study the summit set, the super summit set, the improved super summit set algorithm which utilises minimal simple elements, the ultra summit set, improvements to the ultra summit set solution using graph theory, and lastly the set of sliding circuits. As part of this investigation, we also study normal forms of braids, partial orders on the braid group, and the Garside group which generalises the braid group. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/37181 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:12.104Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/37181 Solutions to the conjugacy search and decision problems in the braid group using finite conjugacy class invariants Erasmus, Sane´ Blackman, Claire Erwin, David Applied Mathematics For two braids, A, B ∈ Bn, the conjugacy decision problem asks whether another braid X ∈ Bn exists such that X−1 A X = B. If we know A, B ∈ Bn are indeed conjugate, the conjugacy search problem asks us to find a braid Y ∈ Bn such that Y −1 A Y = B. In this dissertation we investigate a number of solutions to the conjugacy search problem and conjugacy decision problem in the braid group, all of which use finite invariant subsets of the conjugacy class. In particular, we study the summit set, the super summit set, the improved super summit set algorithm which utilises minimal simple elements, the ultra summit set, improvements to the ultra summit set solution using graph theory, and lastly the set of sliding circuits. As part of this investigation, we also study normal forms of braids, partial orders on the braid group, and the Garside group which generalises the braid group. 2023-03-03T09:34:25Z 2023-03-03T09:34:25Z 2022 2023-02-20T12:44:04Z Master Thesis Masters MSc http://hdl.handle.net/11427/37181 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Applied Mathematics Erasmus, Sane´ Solutions to the conjugacy search and decision problems in the braid group using finite conjugacy class invariants |
| thesis_degree_str | Master's |
| title | Solutions to the conjugacy search and decision problems in the braid group using finite conjugacy class invariants |
| title_full | Solutions to the conjugacy search and decision problems in the braid group using finite conjugacy class invariants |
| title_fullStr | Solutions to the conjugacy search and decision problems in the braid group using finite conjugacy class invariants |
| title_full_unstemmed | Solutions to the conjugacy search and decision problems in the braid group using finite conjugacy class invariants |
| title_short | Solutions to the conjugacy search and decision problems in the braid group using finite conjugacy class invariants |
| title_sort | solutions to the conjugacy search and decision problems in the braid group using finite conjugacy class invariants |
| topic | Applied Mathematics |
| url | http://hdl.handle.net/11427/37181 |
| work_keys_str_mv | AT erasmussane solutionstotheconjugacysearchanddecisionproblemsinthebraidgroupusingfiniteconjugacyclassinvariants |