On the Ozsváth-Szabó $d$-invariants for almost simple linear graphs
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912976181657600 |
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| author | Suzuki, Tatsumasa |
| author_facet | Suzuki, Tatsumasa |
| contents | Karakurt and Şavk computed the Ozsváth-Szabó $d$-invariants of Brieskorn homology $3$-spheres arising as surgeries on almost simple linear graphs. In this paper, we refine their formula for these $d$-invariants. Furthermore, we present infinite families of examples for which the inequalities appearing in this refinement are equalities, as well as infinite families for which they are strict. As an application, we derive consequences for the knot concordance group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14279 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Ozsváth-Szabó $d$-invariants for almost simple linear graphs Suzuki, Tatsumasa Geometric Topology 57K30, 57K31, 57R58 Karakurt and Şavk computed the Ozsváth-Szabó $d$-invariants of Brieskorn homology $3$-spheres arising as surgeries on almost simple linear graphs. In this paper, we refine their formula for these $d$-invariants. Furthermore, we present infinite families of examples for which the inequalities appearing in this refinement are equalities, as well as infinite families for which they are strict. As an application, we derive consequences for the knot concordance group. |
| title | On the Ozsváth-Szabó $d$-invariants for almost simple linear graphs |
| topic | Geometric Topology 57K30, 57K31, 57R58 |
| url | https://arxiv.org/abs/2310.14279 |