Contact 3-manifolds with infinitely many rational homology ball Stein fillings

Abstract

We construct the first examples of contact $3$-manifolds admitting infinitely many pairwise non-homeomorphic Stein fillings which are rational homology balls. Our examples are planar. They are obtained by a simple modification of Baykur's recent planar contact $3$-manifold (Y,ξ) with infinitely many pairwise non-homeomorphic Stein fillings, and the fillings are distinguished by their fundamental groups. For one of these rational homology balls we give an explicit Kirby diagram, with a single $1$-handle and a single $2$-handle attached along a trefoil, which exhibits its boundary as (0,−8)-surgery on a two-component link. We also identify the smooth topology of Baykur's example: Y is obtained by (0,−8)-surgery on the link 7²₄, and it is Seifert fibered over the Klein bottle with one exceptional fiber. Finally, we construct further Stein fillings of (Y,ξ), which realize all the groups ℤ/mrtimes₋₁ℤ, m≥0, as their fundamental groups.

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BibTeX RIS

BibTeX

@misc{ozbagci2026contact,
  title = {{Contact 3-manifolds with infinitely many rational homology ball Stein fillings}},
  author = {Burak Ozbagci},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34381},
  eprint = {2610.34381},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34381},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Contact 3-manifolds with infinitely many rational homology ball Stein fillings
AU  - Burak Ozbagci
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34381
UR  - https://arxiv.org/abs/2610.34381
AB  - We construct the first examples of contact $3$-manifolds admitting infinitely many pairwise non-homeomorphic Stein fillings which are rational homology balls. Our examples are planar. They are obtained by a simple modification of Baykur's recent planar contact $3$-manifold (Y,ξ) with infinitely many pairwise non-homeomorphic Stein fillings, and the fillings are distinguished by their fundamental groups. For one of these rational homology balls we give an explicit Kirby diagram, with a single $1$-handle and a single $2$-handle attached along a trefoil, which exhibits its boundary as (0,−8)-surgery on a two-component link. We also identify the smooth topology of Baykur's example: Y is obtained by (0,−8)-surgery on the link 7^2_4, and it is Seifert fibered over the Klein bottle with one exceptional fiber. Finally, we construct further Stein fillings of (Y,ξ), which realize all the groups ℤ/mrtimes_−1ℤ, m≥0, as their fundamental groups.
ER  -

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