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The three-dimensional symplectization question for small Seifert L-spaces and further classes

  • Nobuo Iida
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Abstract

We solve the three-dimensional symplectization question for several examples. These include small Seifert fibered L-spaces, a family of Whitehead-link surgery L-spaces, S1× S2, certain surgeries on the figure-eight knot, explicit families of Brieskorn spheres, and arbitrary finite connected sums mixing these manifolds. In particular, the result covers the Weeks manifold and infinitely many hyperbolic L-spaces. The main symplectic step is to construct Liouville cobordisms in both directions from a symplectomorphism of symplectizations. The resulting preservation of strong fillability and of the vanishing of the monopole Floer contact invariant, together with the comparison with the Heegaard Floer contact invariant, connected-sum formulas, and classification results for tight contact structures, proves the stated rigidity results.

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Cite

BibTeXRIS
BibTeX
@misc{iida2026threedimensional,
  title = {{The three-dimensional symplectization question for small Seifert L-spaces and further classes}},
  author = {Nobuo Iida},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29534},
  eprint = {2609.29534},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29534},
}
RIS
TY  - UNPB
TI  - The three-dimensional symplectization question for small Seifert L-spaces and further classes
AU  - Nobuo Iida
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.29534
UR  - https://arxiv.org/abs/2609.29534
AB  - We solve the three-dimensional symplectization question for several examples. These include small Seifert fibered L-spaces, a family of Whitehead-link surgery L-spaces, S^1× S^2, certain surgeries on the figure-eight knot, explicit families of Brieskorn spheres, and arbitrary finite connected sums mixing these manifolds. In particular, the result covers the Weeks manifold and infinitely many hyperbolic L-spaces. The main symplectic step is to construct Liouville cobordisms in both directions from a symplectomorphism of symplectizations. The resulting preservation of strong fillability and of the vanishing of the monopole Floer contact invariant, together with the comparison with the Heegaard Floer contact invariant, connected-sum formulas, and classification results for tight contact structures, proves the stated rigidity results.
ER  -