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PreprintCC0arXiv

Braided Multisections and Akhmedov's Fake Quadrics

  • Anar Akhmedov
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Abstract

We give handlebody decompositions of the complements of the cyclic multisections in Σg× S2 constructed in~\cite{AB}. The 2-handle framings are induced by the product coordinates. We compute the integral homology of the complements from their handle chain complexes, including the torsion subgroup of H2. For the degree pairs (3,3) and (2,4), we specify surface diffeomorphisms inducing the maps on first homology prescribed in~\cite{AY} and recover the integral first homology groups (Z/3)2⊕Z/(3m) and (Z/2)2⊕Z/(4m), respectively, for m≥1. For the symmetric m=1 sum, we also give a simultaneous surface diagram of the relative product attachments and identify their product framings with the surface framings. The resulting symplectic sums are aspherical and symplectically minimal, and have the rational cohomology ring of S2× S2.

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Cite

BibTeXRIS
BibTeX
@misc{akhmedov2026braided,
  title = {{Braided Multisections and Akhmedov's Fake Quadrics}},
  author = {Anar Akhmedov},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06949},
  eprint = {2611.06949},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06949},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Braided Multisections and Akhmedov's Fake Quadrics
AU  - Anar Akhmedov
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.06949
UR  - https://arxiv.org/abs/2611.06949
AB  - We give handlebody decompositions of the complements of the cyclic multisections in Σ_g× S^2 constructed in~\cite{AB}. The 2-handle framings are induced by the product coordinates. We compute the integral homology of the complements from their handle chain complexes, including the torsion subgroup of H_2. For the degree pairs (3,3) and (2,4), we specify surface diffeomorphisms inducing the maps on first homology prescribed in~\cite{AY} and recover the integral first homology groups (Z/3)^2⊕Z/(3m) and (Z/2)^2⊕Z/(4m), respectively, for m≥1. For the symmetric m=1 sum, we also give a simultaneous surface diagram of the relative product attachments and identify their product framings with the surface framings. The resulting symplectic sums are aspherical and symplectically minimal, and have the rational cohomology ring of S^2× S^2.
ER  -