The Reidemeister graph is a complete knot invariant
We describe two locally finite graphs naturally associated to each knot type K, called Reidemeister graphs. We determine several local and global properties of these graphs and prove that in one case the graph-isomorphism type is a complete knot invariant up to mirroring. Lastly, we introduce anoth...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Mathematical Sciences Publishers
2020
|
| _version_ | 1797094464868581376 |
|---|---|
| author | Barbensi, A Celoria, D |
| author_facet | Barbensi, A Celoria, D |
| author_sort | Barbensi, A |
| collection | OXFORD |
| description | We describe two locally finite graphs naturally associated to each knot type
K, called Reidemeister graphs. We determine several local and global properties of these graphs and prove that in one case the graph-isomorphism type is a complete knot invariant up to mirroring. Lastly, we introduce another object, relating the Reidemeister and Gordian graphs, and determine some of its properties. |
| first_indexed | 2024-03-07T04:14:26Z |
| format | Journal article |
| id | oxford-uuid:c8ef9c90-e7a5-4276-8de7-284240beb53f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:14:26Z |
| publishDate | 2020 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | oxford-uuid:c8ef9c90-e7a5-4276-8de7-284240beb53f2022-03-27T06:55:32ZThe Reidemeister graph is a complete knot invariantJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c8ef9c90-e7a5-4276-8de7-284240beb53fEnglishSymplectic Elements at OxfordMathematical Sciences Publishers2020Barbensi, ACeloria, DWe describe two locally finite graphs naturally associated to each knot type K, called Reidemeister graphs. We determine several local and global properties of these graphs and prove that in one case the graph-isomorphism type is a complete knot invariant up to mirroring. Lastly, we introduce another object, relating the Reidemeister and Gordian graphs, and determine some of its properties. |
| spellingShingle | Barbensi, A Celoria, D The Reidemeister graph is a complete knot invariant |
| title | The Reidemeister graph is a complete knot invariant |
| title_full | The Reidemeister graph is a complete knot invariant |
| title_fullStr | The Reidemeister graph is a complete knot invariant |
| title_full_unstemmed | The Reidemeister graph is a complete knot invariant |
| title_short | The Reidemeister graph is a complete knot invariant |
| title_sort | reidemeister graph is a complete knot invariant |
| work_keys_str_mv | AT barbensia thereidemeistergraphisacompleteknotinvariant AT celoriad thereidemeistergraphisacompleteknotinvariant AT barbensia reidemeistergraphisacompleteknotinvariant AT celoriad reidemeistergraphisacompleteknotinvariant |