Betti numbers and torsions in homology groups of double coverings
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914800977575936 |
|---|---|
| author | Ishibashi, Suguru Sugawara, Sakumi Yoshinaga, Masahiko |
| author_facet | Ishibashi, Suguru Sugawara, Sakumi Yoshinaga, Masahiko |
| contents | Papadima and Suciu proved an inequality between the ranks of the cohomology groups of the Aomoto complex with finite field coefficients and the twisted cohomology groups, and conjectured that they are actually equal for certain cases associated with the Milnor fiber of the arrangement. Recently, an arrangement (the icosidodecahedral arrangement) with the following two peculiar properties was found: (i) the strict version of Papadima-Suciu's inequality holds, and (ii) the first integral homology of the Milnor fiber has a non-trivial $2$-torsion. In this paper, we investigate the relationship between these two properties for double covering spaces. We prove that (i) and (ii) are actually equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02236 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Betti numbers and torsions in homology groups of double coverings Ishibashi, Suguru Sugawara, Sakumi Yoshinaga, Masahiko Geometric Topology Combinatorics 52C35, 20F55 Papadima and Suciu proved an inequality between the ranks of the cohomology groups of the Aomoto complex with finite field coefficients and the twisted cohomology groups, and conjectured that they are actually equal for certain cases associated with the Milnor fiber of the arrangement. Recently, an arrangement (the icosidodecahedral arrangement) with the following two peculiar properties was found: (i) the strict version of Papadima-Suciu's inequality holds, and (ii) the first integral homology of the Milnor fiber has a non-trivial $2$-torsion. In this paper, we investigate the relationship between these two properties for double covering spaces. We prove that (i) and (ii) are actually equivalent. |
| title | Betti numbers and torsions in homology groups of double coverings |
| topic | Geometric Topology Combinatorics 52C35, 20F55 |
| url | https://arxiv.org/abs/2209.02236 |