Torres-type formulas for link signatures
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912278622765056 |
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| author | Cimasoni, David Markiewicz, Maciej Politarczyk, Wojciech |
| author_facet | Cimasoni, David Markiewicz, Maciej Politarczyk, Wojciech |
| contents | We investigate the limits of the multivariable signature function $σ_L$ of a $μ$-component link $L$ as some variable tends to $1$ via two different approaches: a three-dimensional and a four-dimensional one. The first uses the definition of $σ_L$ by generalized Seifert surfaces and forms. The second relies on a new extension of $σ_L$ from its usual domain $(S^1\setminus\{1\})^μ$ to the full torus $\mathbb{T}^μ$ together with a Torres-type formula for $σ_L$, results which are of independent interest. Among several consequences, we obtain new estimates on the value of the Levine-Tristram signature of a link close to $1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02347 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Torres-type formulas for link signatures Cimasoni, David Markiewicz, Maciej Politarczyk, Wojciech Geometric Topology 57K10 (Primary) 57M05, 55N25 (Secondary) We investigate the limits of the multivariable signature function $σ_L$ of a $μ$-component link $L$ as some variable tends to $1$ via two different approaches: a three-dimensional and a four-dimensional one. The first uses the definition of $σ_L$ by generalized Seifert surfaces and forms. The second relies on a new extension of $σ_L$ from its usual domain $(S^1\setminus\{1\})^μ$ to the full torus $\mathbb{T}^μ$ together with a Torres-type formula for $σ_L$, results which are of independent interest. Among several consequences, we obtain new estimates on the value of the Levine-Tristram signature of a link close to $1$. |
| title | Torres-type formulas for link signatures |
| topic | Geometric Topology 57K10 (Primary) 57M05, 55N25 (Secondary) |
| url | https://arxiv.org/abs/2304.02347 |