Floer homology and non-fibered knot detection
We prove for the first time that knot Floer homology and Khovanov homology can detect non-fibered knots and that HOMFLY homology detects infinitely many knots; these theories were previously known to detect a mere six knots, all fibered. These results rely on our main technical theorem, which gives...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Pi |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508624000283/type/journal_article |
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| author | John A. Baldwin Steven Sivek |
| author_facet | John A. Baldwin Steven Sivek |
| author_sort | John A. Baldwin |
| collection | DOAJ |
| description | We prove for the first time that knot Floer homology and Khovanov homology can detect non-fibered knots and that HOMFLY homology detects infinitely many knots; these theories were previously known to detect a mere six knots, all fibered. These results rely on our main technical theorem, which gives a complete classification of genus-1 knots in the 3-sphere whose knot Floer homology in the top Alexander grading is 2-dimensional. We discuss applications of this classification to problems in Dehn surgery which are carried out in two sequels. These include a proof that
$0$
-surgery characterizes infinitely many knots, generalizing results of Gabai from his 1987 resolution of the Property R Conjecture. |
| format | Article |
| id | doaj-art-893c6b17488b4a06abac0b57e88d10db |
| institution | Kabale University |
| issn | 2050-5086 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Pi |
| spelling | doaj-art-893c6b17488b4a06abac0b57e88d10db2025-01-20T10:30:49ZengCambridge University PressForum of Mathematics, Pi2050-50862025-01-011310.1017/fmp.2024.28Floer homology and non-fibered knot detectionJohn A. Baldwin0https://orcid.org/0000-0002-1902-3523Steven Sivek1https://orcid.org/0000-0003-0230-8087Department of Mathematics, Boston College, Maloney Hall, Fifth Floor, Chestnut Hill, MA, 02467-3806, USADepartment of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom; E-mail:We prove for the first time that knot Floer homology and Khovanov homology can detect non-fibered knots and that HOMFLY homology detects infinitely many knots; these theories were previously known to detect a mere six knots, all fibered. These results rely on our main technical theorem, which gives a complete classification of genus-1 knots in the 3-sphere whose knot Floer homology in the top Alexander grading is 2-dimensional. We discuss applications of this classification to problems in Dehn surgery which are carried out in two sequels. These include a proof that $0$ -surgery characterizes infinitely many knots, generalizing results of Gabai from his 1987 resolution of the Property R Conjecture.https://www.cambridge.org/core/product/identifier/S2050508624000283/type/journal_article57K1857K1057R58 |
| spellingShingle | John A. Baldwin Steven Sivek Floer homology and non-fibered knot detection Forum of Mathematics, Pi 57K18 57K10 57R58 |
| title | Floer homology and non-fibered knot detection |
| title_full | Floer homology and non-fibered knot detection |
| title_fullStr | Floer homology and non-fibered knot detection |
| title_full_unstemmed | Floer homology and non-fibered knot detection |
| title_short | Floer homology and non-fibered knot detection |
| title_sort | floer homology and non fibered knot detection |
| topic | 57K18 57K10 57R58 |
| url | https://www.cambridge.org/core/product/identifier/S2050508624000283/type/journal_article |
| work_keys_str_mv | AT johnabaldwin floerhomologyandnonfiberedknotdetection AT stevensivek floerhomologyandnonfiberedknotdetection |