Geography of irreducible 4-manifolds with order two fundamental group
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915146360684544 |
|---|---|
| author | Arabadji, Mihail Morgan, Porter |
| author_facet | Arabadji, Mihail Morgan, Porter |
| contents | Let $R$ be a closed, oriented topological 4-manifold whose Euler characteristic and signature are denoted by $e$ and $σ$. We show that if $R$ has order two $π_1$, odd intersection form, and $2e + 3σ\geq 0$, then for all but seven $(e, σ)$ coordinates, $R$ admits an irreducible smooth structure. We accomplish this by performing a variety of operations on irreducible simply-connected 4-manifolds to build 4-manifolds with order two $π_1$. These techniques include torus surgeries, symplectic fiber sums, rational blow-downs, and numerous constructions of Lefschetz fibrations, including a new approach to equivariant fiber summing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geography of irreducible 4-manifolds with order two fundamental group Arabadji, Mihail Morgan, Porter Geometric Topology Let $R$ be a closed, oriented topological 4-manifold whose Euler characteristic and signature are denoted by $e$ and $σ$. We show that if $R$ has order two $π_1$, odd intersection form, and $2e + 3σ\geq 0$, then for all but seven $(e, σ)$ coordinates, $R$ admits an irreducible smooth structure. We accomplish this by performing a variety of operations on irreducible simply-connected 4-manifolds to build 4-manifolds with order two $π_1$. These techniques include torus surgeries, symplectic fiber sums, rational blow-downs, and numerous constructions of Lefschetz fibrations, including a new approach to equivariant fiber summing. |
| title | Geography of irreducible 4-manifolds with order two fundamental group |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2502.07689 |