Torsion in the knot concordance group and cabling
We define a nontrivial modulo 2 valued additive concordance invariant defined on the torsion subgroup of the knot concordance group using involutive knot Floer package. For knots not contained in its kernel, we prove that their iterated (odd,1)-cables have infinite order in the concordance group and...
| Автори: | , |
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| Формат: | Journal article |
| Мова: | English |
| Опубліковано: |
EMS Press
2024
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| _version_ | 1826314893491437568 |
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| author | Kang, S Park, J |
| author_facet | Kang, S Park, J |
| author_sort | Kang, S |
| collection | OXFORD |
| description | We define a nontrivial modulo 2 valued additive concordance invariant defined on the torsion subgroup of the knot concordance group using involutive knot Floer package. For knots not contained in its kernel, we prove that their iterated (odd,1)-cables have infinite order in the concordance group and, among them, infinitely many are linearly independent. Furthermore, by taking (2,1)-cables of the aforementioned knots, we present an infinite family of knots which are strongly rationally slice but not slice. |
| first_indexed | 2024-12-09T03:14:26Z |
| format | Journal article |
| id | oxford-uuid:2fd0045f-935e-482c-a39e-7964a5d2f99b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:14:26Z |
| publishDate | 2024 |
| publisher | EMS Press |
| record_format | dspace |
| spelling | oxford-uuid:2fd0045f-935e-482c-a39e-7964a5d2f99b2024-10-17T12:53:53ZTorsion in the knot concordance group and cablingJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2fd0045f-935e-482c-a39e-7964a5d2f99bEnglishSymplectic ElementsEMS Press2024Kang, SPark, JWe define a nontrivial modulo 2 valued additive concordance invariant defined on the torsion subgroup of the knot concordance group using involutive knot Floer package. For knots not contained in its kernel, we prove that their iterated (odd,1)-cables have infinite order in the concordance group and, among them, infinitely many are linearly independent. Furthermore, by taking (2,1)-cables of the aforementioned knots, we present an infinite family of knots which are strongly rationally slice but not slice. |
| spellingShingle | Kang, S Park, J Torsion in the knot concordance group and cabling |
| title | Torsion in the knot concordance group and cabling |
| title_full | Torsion in the knot concordance group and cabling |
| title_fullStr | Torsion in the knot concordance group and cabling |
| title_full_unstemmed | Torsion in the knot concordance group and cabling |
| title_short | Torsion in the knot concordance group and cabling |
| title_sort | torsion in the knot concordance group and cabling |
| work_keys_str_mv | AT kangs torsionintheknotconcordancegroupandcabling AT parkj torsionintheknotconcordancegroupandcabling |