On T-positive links
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914553868058624 |
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| author | Bode, Benjamin Truöl, Paula |
| author_facet | Bode, Benjamin Truöl, Paula |
| contents | T-positive links form a subset of strongly quasipositive links that strictly contains the set of all non-split braid positive links. Analogous to Baader's characterisation of positive links as precisely the strongly quasipositive and homogeneous links, we show that T-positive links are precisely the strongly quasipositive links that are the closures of T-homogeneous braids. This complements previous characterizations of T-positive links by Rudolph and Banfield as links arising as boundaries of positive Hopf-plumbed baskets, or closures of staircase braids. We examine the behavior of T-positive links under cabling operations and connected sums, and demonstrate that all strongly quasipositive, fibered knots with at most 12 crossings are T-positive. Additionally, we compare T-positivity with other positivity notions for links and compile open questions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10502 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On T-positive links Bode, Benjamin Truöl, Paula Geometric Topology 57K10 (Primary) 20F36 (Secondary) T-positive links form a subset of strongly quasipositive links that strictly contains the set of all non-split braid positive links. Analogous to Baader's characterisation of positive links as precisely the strongly quasipositive and homogeneous links, we show that T-positive links are precisely the strongly quasipositive links that are the closures of T-homogeneous braids. This complements previous characterizations of T-positive links by Rudolph and Banfield as links arising as boundaries of positive Hopf-plumbed baskets, or closures of staircase braids. We examine the behavior of T-positive links under cabling operations and connected sums, and demonstrate that all strongly quasipositive, fibered knots with at most 12 crossings are T-positive. Additionally, we compare T-positivity with other positivity notions for links and compile open questions. |
| title | On T-positive links |
| topic | Geometric Topology 57K10 (Primary) 20F36 (Secondary) |
| url | https://arxiv.org/abs/2605.10502 |