On smooth structures over $4$-manifolds with fundamental group of even order
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914435335979008 |
|---|---|
| author | Ladu, Roberto Tagliente, Simone |
| author_facet | Ladu, Roberto Tagliente, Simone |
| contents | We show that any topological, closed, oriented, non-spin $4$-manifold with fundamental group $\mathbb{Z}_{4k}$ and $\min(b_2^+, b_2^-)\geq 15$, has either none or infinitely many distinct smooth structures. Furthermore, we construct infinitely many non-diffeomorphic, irreducible, smooth structures on manifolds with signature zero, $b_2^+$ even and fundamental group $\mathbb{Z}_2\times G$, for any finite group $G$. This extends the results of Baykur-Stipsicz-Szabó. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29794 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On smooth structures over $4$-manifolds with fundamental group of even order Ladu, Roberto Tagliente, Simone Geometric Topology 57R55, 57K40 We show that any topological, closed, oriented, non-spin $4$-manifold with fundamental group $\mathbb{Z}_{4k}$ and $\min(b_2^+, b_2^-)\geq 15$, has either none or infinitely many distinct smooth structures. Furthermore, we construct infinitely many non-diffeomorphic, irreducible, smooth structures on manifolds with signature zero, $b_2^+$ even and fundamental group $\mathbb{Z}_2\times G$, for any finite group $G$. This extends the results of Baykur-Stipsicz-Szabó. |
| title | On smooth structures over $4$-manifolds with fundamental group of even order |
| topic | Geometric Topology 57R55, 57K40 |
| url | https://arxiv.org/abs/2603.29794 |