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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2409.02192 |
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| _version_ | 1866909635530719232 |
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| author | Hendricks, Kristen Mallick, Abhishek |
| author_facet | Hendricks, Kristen Mallick, Abhishek |
| contents | We prove a formula for the involutive concordance invariants of the cabled knots in terms of that of the companion knot and the pattern knot. As a consequence, we show that any iterated cable of a knot with parameters of the form (odd,1) is not smoothly slice as long as either of the involutive concordance invariants of the knot is nonzero. Our formula also gives new bounds for the unknotting number of a cabled knot, which are sometimes stronger than other known bounds coming from knot Floer homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02192 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on cables and the involutive concordance invariants Hendricks, Kristen Mallick, Abhishek Geometric Topology 57K18 We prove a formula for the involutive concordance invariants of the cabled knots in terms of that of the companion knot and the pattern knot. As a consequence, we show that any iterated cable of a knot with parameters of the form (odd,1) is not smoothly slice as long as either of the involutive concordance invariants of the knot is nonzero. Our formula also gives new bounds for the unknotting number of a cabled knot, which are sometimes stronger than other known bounds coming from knot Floer homology. |
| title | A note on cables and the involutive concordance invariants |
| topic | Geometric Topology 57K18 |
| url | https://arxiv.org/abs/2409.02192 |