The computational complexity of knot genus in a fixed 3-manifold
We show that the problem of deciding whether a knot in a fixed closed orientable 3-dimensional manifold bounds a surface of genus at most <i>g</i> is in co-NP. This answers a question of Agol, Hass and Thurston in 2002. Previously, this was known for rational homology 3-spheres, by the...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
London Mathematical Society
2023
|
| _version_ | 1826310361088786432 |
|---|---|
| author | Lackenby, M Yazdi, M |
| author_facet | Lackenby, M Yazdi, M |
| author_sort | Lackenby, M |
| collection | OXFORD |
| description | We show that the problem of deciding whether a knot in a fixed closed orientable 3-dimensional manifold bounds a surface of genus at most <i>g</i> is in co-NP. This answers a question of Agol, Hass and Thurston in 2002. Previously, this was known for rational homology 3-spheres, by the work of the first author. |
| first_indexed | 2024-03-07T07:50:47Z |
| format | Journal article |
| id | oxford-uuid:f8a08a8b-6c67-4134-95bb-6eb570c0a57c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:50:47Z |
| publishDate | 2023 |
| publisher | London Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:f8a08a8b-6c67-4134-95bb-6eb570c0a57c2023-07-04T09:46:41ZThe computational complexity of knot genus in a fixed 3-manifoldJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f8a08a8b-6c67-4134-95bb-6eb570c0a57cEnglishSymplectic ElementsLondon Mathematical Society2023Lackenby, MYazdi, MWe show that the problem of deciding whether a knot in a fixed closed orientable 3-dimensional manifold bounds a surface of genus at most <i>g</i> is in co-NP. This answers a question of Agol, Hass and Thurston in 2002. Previously, this was known for rational homology 3-spheres, by the work of the first author. |
| spellingShingle | Lackenby, M Yazdi, M The computational complexity of knot genus in a fixed 3-manifold |
| title | The computational complexity of knot genus in a fixed 3-manifold |
| title_full | The computational complexity of knot genus in a fixed 3-manifold |
| title_fullStr | The computational complexity of knot genus in a fixed 3-manifold |
| title_full_unstemmed | The computational complexity of knot genus in a fixed 3-manifold |
| title_short | The computational complexity of knot genus in a fixed 3-manifold |
| title_sort | computational complexity of knot genus in a fixed 3 manifold |
| work_keys_str_mv | AT lackenbym thecomputationalcomplexityofknotgenusinafixed3manifold AT yazdim thecomputationalcomplexityofknotgenusinafixed3manifold AT lackenbym computationalcomplexityofknotgenusinafixed3manifold AT yazdim computationalcomplexityofknotgenusinafixed3manifold |