Double coverings of arrangement complements and $2$-torsion in Milnor fiber homology
| Autor: | Masahiko Yoshinaga |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Hyperplane arrangements Betti number General Mathematics Icosidodecahedron Algebraic geometry Homology (mathematics) Mathematics - Algebraic Geometry Mathematics - Geometric Topology Transfer map FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Combinatorics Mathematics - Algebraic Topology Algebraic Geometry (math.AG) Mathematics Exact sequence Geometric Topology (math.GT) Milnor fiber Hyperplane Monodromy Torsion (algebra) Combinatorics (math.CO) Aomoto complex |
| Popis: | We prove that the mod $2$ Betti numbers of double coverings of a complex hyperplane arrangement complement are combinatorially determined. The proof is based on a relation between the mod $2$ Aomoto complex and the transfer long exact sequence. Applying the above result to the icosidodecahedral arrangement ($16$ planes in the three dimensional space related to the icosidodecahedron), we conclude that the first homology of the Milnor fiber has non-trivial $2$-torsion. 14 pages, 5 figures, to appear in European Journal of Mathematics |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|