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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.09319 |
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Table of 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 $d=4$.