Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.09319 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914600759328768 |
|---|---|
| author | Bais, Valentina Piergallini, Riccardo Zuddas, Daniele |
| author_facet | Bais, Valentina Piergallini, Riccardo Zuddas, Daniele |
| contents | We show that every closed connected non-orientable PL $4$-manifold $X$ is a simple branched covering of $\RP^4$. We also show that $X$ is a simple branched covering of the twisted $S^3$-bundle $S^1 \simtimes S^3$ if and only if the first Stiefel--Whitney class $w_1(X)$ admits an integral lift. In both cases, the degree of the covering can be any number $d \geq 4$, provided that $d$ has the same parity of the Stiefel--Whitney number $w_1^4[X]$ in the case of $\RP^4$. Moreover, the branch set can be assumed to be non-singular if $d \geq 5$ and to have just nodal singularities if $d=4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09319 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Branched covering representation of non-orientable $4$-manifolds Bais, Valentina Piergallini, Riccardo Zuddas, Daniele Geometric Topology We show that every closed connected non-orientable PL $4$-manifold $X$ is a simple branched covering of $\RP^4$. We also show that $X$ is a simple branched covering of the twisted $S^3$-bundle $S^1 \simtimes S^3$ if and only if the first Stiefel--Whitney class $w_1(X)$ admits an integral lift. In both cases, the degree of the covering can be any number $d \geq 4$, provided that $d$ has the same parity of the Stiefel--Whitney number $w_1^4[X]$ in the case of $\RP^4$. Moreover, the branch set can be assumed to be non-singular if $d \geq 5$ and to have just nodal singularities if $d=4$. |
| title | Branched covering representation of non-orientable $4$-manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2509.09319 |