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| Auteurs principaux: | , |
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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2605.23086 |
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| _version_ | 1866917522833408000 |
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| author | Davis, Christopher W. Park, JungHwan |
| author_facet | Davis, Christopher W. Park, JungHwan |
| contents | We define a sequence of integer-valued invariants $γ^k(L)$ for a $3$-component link $L$. We prove that the resulting $γ$-invariants are invariant under concordance, and more generally under weak cobordism, and that they lift certain Milnor invariants of 3-component links. To establish this, we introduce an invariant $h(L)$, a $3$-component analogue of the Kojima--Yamasaki $η$-invariant, and show that it recovers the $γ$-invariants. As applications, we obtain a weak-cobordism classification when the distinguished component has trivial Alexander polynomial and characterize knots that bound continuously embedded disks in $B^4$ whose complements have fundamental group $\mathbb{Z}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23086 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lifting Milnor Invariants for 3-Component Links Davis, Christopher W. Park, JungHwan Geometric Topology 57K10 We define a sequence of integer-valued invariants $γ^k(L)$ for a $3$-component link $L$. We prove that the resulting $γ$-invariants are invariant under concordance, and more generally under weak cobordism, and that they lift certain Milnor invariants of 3-component links. To establish this, we introduce an invariant $h(L)$, a $3$-component analogue of the Kojima--Yamasaki $η$-invariant, and show that it recovers the $γ$-invariants. As applications, we obtain a weak-cobordism classification when the distinguished component has trivial Alexander polynomial and characterize knots that bound continuously embedded disks in $B^4$ whose complements have fundamental group $\mathbb{Z}$. |
| title | Lifting Milnor Invariants for 3-Component Links |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2605.23086 |