Distinguishing slice disks using knot Floer homology
We study the classification of slice disks of knots up to isotopy and diffeomorphism using an invariant in knot Floer homology. We compute the invariant of a slice disk obtained by deform-spinning, and show that it can be effectively used to distinguish non-isotopic slice disks with diffeomorphic co...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer
2019
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| _version_ | 1826257294582611968 |
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| author | Juhasz, A Zemke, I |
| author_facet | Juhasz, A Zemke, I |
| author_sort | Juhasz, A |
| collection | OXFORD |
| description | We study the classification of slice disks of knots up to isotopy and diffeomorphism using an invariant in knot Floer homology. We compute the invariant of a slice disk obtained by deform-spinning, and show that it can be effectively used to distinguish non-isotopic slice disks with diffeomorphic complements. Given a slice disk of a composite knot, we define a numerical stable diffeomorphism invariant called the rank. This can be used to show that a slice disk is not a boundary connected sum, and to give lower bounds on the complexity of certain hyperplane sections of the slice disk. |
| first_indexed | 2024-03-06T18:15:53Z |
| format | Journal article |
| id | oxford-uuid:049c2746-b2d3-49ca-98f4-b0fea6bf0e4f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:15:53Z |
| publishDate | 2019 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:049c2746-b2d3-49ca-98f4-b0fea6bf0e4f2022-03-26T08:52:42ZDistinguishing slice disks using knot Floer homologyJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:049c2746-b2d3-49ca-98f4-b0fea6bf0e4fEnglishSymplectic Elements at OxfordSpringer2019Juhasz, AZemke, IWe study the classification of slice disks of knots up to isotopy and diffeomorphism using an invariant in knot Floer homology. We compute the invariant of a slice disk obtained by deform-spinning, and show that it can be effectively used to distinguish non-isotopic slice disks with diffeomorphic complements. Given a slice disk of a composite knot, we define a numerical stable diffeomorphism invariant called the rank. This can be used to show that a slice disk is not a boundary connected sum, and to give lower bounds on the complexity of certain hyperplane sections of the slice disk. |
| spellingShingle | Juhasz, A Zemke, I Distinguishing slice disks using knot Floer homology |
| title | Distinguishing slice disks using knot Floer homology |
| title_full | Distinguishing slice disks using knot Floer homology |
| title_fullStr | Distinguishing slice disks using knot Floer homology |
| title_full_unstemmed | Distinguishing slice disks using knot Floer homology |
| title_short | Distinguishing slice disks using knot Floer homology |
| title_sort | distinguishing slice disks using knot floer homology |
| work_keys_str_mv | AT juhasza distinguishingslicedisksusingknotfloerhomology AT zemkei distinguishingslicedisksusingknotfloerhomology |