The crossing number of composite knots
It is a very old conjecture that the crossing number of knots is additive under connected sum. In other words, if K#K' is the connected sum of knots K and K', then does the equality c(K#K') = c(K) + c(K') hold? We prove that c(K#K') is at most c(K) + c(K') and at least...
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| Materyal Türü: | Journal article |
| Baskı/Yayın Bilgisi: |
2008
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| _version_ | 1826281074016124928 |
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| author | Lackenby, M |
| author_facet | Lackenby, M |
| author_sort | Lackenby, M |
| collection | OXFORD |
| description | It is a very old conjecture that the crossing number of knots is additive under connected sum. In other words, if K#K' is the connected sum of knots K and K', then does the equality c(K#K') = c(K) + c(K') hold? We prove that c(K#K') is at most c(K) + c(K') and at least (c(K) + c(K'))/152. |
| first_indexed | 2024-03-07T00:23:18Z |
| format | Journal article |
| id | oxford-uuid:7d4538d5-86a5-476d-afb8-d26125daa336 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:23:18Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | oxford-uuid:7d4538d5-86a5-476d-afb8-d26125daa3362022-03-26T21:02:34ZThe crossing number of composite knotsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7d4538d5-86a5-476d-afb8-d26125daa336Symplectic Elements at Oxford2008Lackenby, MIt is a very old conjecture that the crossing number of knots is additive under connected sum. In other words, if K#K' is the connected sum of knots K and K', then does the equality c(K#K') = c(K) + c(K') hold? We prove that c(K#K') is at most c(K) + c(K') and at least (c(K) + c(K'))/152. |
| spellingShingle | Lackenby, M The crossing number of composite knots |
| title | The crossing number of composite knots |
| title_full | The crossing number of composite knots |
| title_fullStr | The crossing number of composite knots |
| title_full_unstemmed | The crossing number of composite knots |
| title_short | The crossing number of composite knots |
| title_sort | crossing number of composite knots |
| work_keys_str_mv | AT lackenbym thecrossingnumberofcompositeknots AT lackenbym crossingnumberofcompositeknots |