The Iwasawa invariants of $\mathbb{Z}_p^{\,d}$-covers of links
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912713629761536 |
|---|---|
| author | Tateno, Sohei Ueki, Jun |
| author_facet | Tateno, Sohei Ueki, Jun |
| contents | Let $p$ be a prime number and let $d\in \mathbb{Z}_{>0}$. In this paper, following the analogy between knots and primes, we study the $p$-torsion growth in a compatible system of $(\mathbb{Z}/p^n\mathbb{Z})^d$-covers of 3-manifolds and establish several analogues of Cuoco--Monsky's multivariable versions of Iwasawa's class number formula. Our main goal is to establish the Cuoco--Monsky type formula for branched covers of links in rational homology 3-spheres. In addition, we prove the precise formula over integral homology 3-spheres prompted by Greenberg's conjecture. We also derive results on reduced Alexander polynomials and on the Betti number periodicity. Furthermore, we investigate the twisted Whitehead links in $S^3$ and point out that the Iwasawa $μ$-invariant of a $\mathbb{Z}_p^{\,2}$-cover can be an arbitrary non-negative integer. We also calculate the Iwasawa $μ$ and $λ$-invariants of the Alexander polynomials of all links in Rolfsen's table. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03258 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Iwasawa invariants of $\mathbb{Z}_p^{\,d}$-covers of links Tateno, Sohei Ueki, Jun Geometric Topology Number Theory Primary 57M12, 11R23, 20E18, Secondary 57K10, 57M10, 11R29 Let $p$ be a prime number and let $d\in \mathbb{Z}_{>0}$. In this paper, following the analogy between knots and primes, we study the $p$-torsion growth in a compatible system of $(\mathbb{Z}/p^n\mathbb{Z})^d$-covers of 3-manifolds and establish several analogues of Cuoco--Monsky's multivariable versions of Iwasawa's class number formula. Our main goal is to establish the Cuoco--Monsky type formula for branched covers of links in rational homology 3-spheres. In addition, we prove the precise formula over integral homology 3-spheres prompted by Greenberg's conjecture. We also derive results on reduced Alexander polynomials and on the Betti number periodicity. Furthermore, we investigate the twisted Whitehead links in $S^3$ and point out that the Iwasawa $μ$-invariant of a $\mathbb{Z}_p^{\,2}$-cover can be an arbitrary non-negative integer. We also calculate the Iwasawa $μ$ and $λ$-invariants of the Alexander polynomials of all links in Rolfsen's table. |
| title | The Iwasawa invariants of $\mathbb{Z}_p^{\,d}$-covers of links |
| topic | Geometric Topology Number Theory Primary 57M12, 11R23, 20E18, Secondary 57K10, 57M10, 11R29 |
| url | https://arxiv.org/abs/2401.03258 |