A polynomial upper bound on Reidemeister moves
We prove that any diagram of the unknot with c crossings may be reduced to the trivial diagram using at most (236 c)^{11} Reidemeister moves. Moreover, every diagram in this sequence has at most (7 c)^2 crossings. We also prove a similar theorem for split links, which provides a polynomial upper bou...
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| Natura: | Journal article |
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Princeton University, Department of Mathematics
2015
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| _version_ | 1826303299473637376 |
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| author | Lackenby, M |
| author_facet | Lackenby, M |
| author_sort | Lackenby, M |
| collection | OXFORD |
| description | We prove that any diagram of the unknot with c crossings may be reduced to the trivial diagram using at most (236 c)^{11} Reidemeister moves. Moreover, every diagram in this sequence has at most (7 c)^2 crossings. We also prove a similar theorem for split links, which provides a polynomial upper bound on the number of Reidemeister moves required to transform a diagram of the link into a disconnected diagram. |
| first_indexed | 2024-03-07T06:00:33Z |
| format | Journal article |
| id | oxford-uuid:ec086aa0-037b-48b5-abfe-e25ed7ef1b71 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:00:33Z |
| publishDate | 2015 |
| publisher | Princeton University, Department of Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:ec086aa0-037b-48b5-abfe-e25ed7ef1b712022-03-27T11:14:24ZA polynomial upper bound on Reidemeister movesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ec086aa0-037b-48b5-abfe-e25ed7ef1b71Symplectic Elements at OxfordPrinceton University, Department of Mathematics2015Lackenby, MWe prove that any diagram of the unknot with c crossings may be reduced to the trivial diagram using at most (236 c)^{11} Reidemeister moves. Moreover, every diagram in this sequence has at most (7 c)^2 crossings. We also prove a similar theorem for split links, which provides a polynomial upper bound on the number of Reidemeister moves required to transform a diagram of the link into a disconnected diagram. |
| spellingShingle | Lackenby, M A polynomial upper bound on Reidemeister moves |
| title | A polynomial upper bound on Reidemeister moves |
| title_full | A polynomial upper bound on Reidemeister moves |
| title_fullStr | A polynomial upper bound on Reidemeister moves |
| title_full_unstemmed | A polynomial upper bound on Reidemeister moves |
| title_short | A polynomial upper bound on Reidemeister moves |
| title_sort | polynomial upper bound on reidemeister moves |
| work_keys_str_mv | AT lackenbym apolynomialupperboundonreidemeistermoves AT lackenbym polynomialupperboundonreidemeistermoves |