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PreprintCC BY-NC-ND 4.0arXiv

Lifting braids over ℝℙ2 and non-orientable Lefschetz fibrations

  • Valentina Bais
  • Porter Morgan
  • Daniele Zuddas
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Abstract

We show that, given a closed connected non-orientable surface F and a simple branched cover p : F → ℝℙ2 of degree d ≥ 5, every self-diffeomorphism of F is isotopic to the lift of a self-diffeomorphism of ℝℙ2 with respect to p. As an application, we show that every Lefschetz fibration over a connected surface B with ∂ B≠ ∅ and closed non-orientable regular fiber can be expressed as the composition of a simple cover of B× ℝℙ2 branched over a surface braided over B and projection onto the B-factor.

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Cite

BibTeXRIS
BibTeX
@misc{bais2026lifting,
  title = {{Lifting braids over $\mathbbRP^2$ and non-orientable Lefschetz fibrations}},
  author = {Valentina Bais and Porter Morgan and Daniele Zuddas},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10757},
  eprint = {2610.10757},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10757},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Lifting braids over ℝℙ^2 and non-orientable Lefschetz fibrations
AU  - Valentina Bais
AU  - Porter Morgan
AU  - Daniele Zuddas
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10757
UR  - https://arxiv.org/abs/2610.10757
AB  - We show that, given a closed connected non-orientable surface F and a simple branched cover p : F → ℝℙ^2 of degree d ≥ 5, every self-diffeomorphism of F is isotopic to the lift of a self-diffeomorphism of ℝℙ^2 with respect to p. As an application, we show that every Lefschetz fibration over a connected surface B with ∂ B≠ ∅ and closed non-orientable regular fiber can be expressed as the composition of a simple cover of B× ℝℙ^2 branched over a surface braided over B and projection onto the B-factor.
ER  -