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Minimum b2 of symplectic fillings of lens spaces

  • Antony T. H. Fung
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Abstract

We classify lens spaces for which the canonical negative-definite plumbing has minimal b2 among all symplectic fillings of the standard contact structure. The classification is given by 4 infinite families of "forbidden subgraphs" in a manner similar to Aceto-McCoy-Park's work on smooth negative-definite fillings of lens spaces. In particular, no classification of this form can be given using a finite list of forbidden configurations, highlighting a difference between symplectic fillings and smooth negative-definite fillings of lens spaces.

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Cite

BibTeXRIS
BibTeX
@misc{fung2026minimum,
  title = {{Minimum $b_2$ of symplectic fillings of lens spaces}},
  author = {Antony T. H. Fung},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01791},
  eprint = {2609.01791},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01791},
}
RIS
TY  - UNPB
TI  - Minimum b_2 of symplectic fillings of lens spaces
AU  - Antony T. H. Fung
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01791
UR  - https://arxiv.org/abs/2609.01791
AB  - We classify lens spaces for which the canonical negative-definite plumbing has minimal b_2 among all symplectic fillings of the standard contact structure. The classification is given by 4 infinite families of "forbidden subgraphs" in a manner similar to Aceto-McCoy-Park's work on smooth negative-definite fillings of lens spaces. In particular, no classification of this form can be given using a finite list of forbidden configurations, highlighting a difference between symplectic fillings and smooth negative-definite fillings of lens spaces.
ER  -