Pith Number

pith:MN4XPCFJ

pith:2026:MN4XPCFJBH6J7QRA5QFFT6SJ2T

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Brieskorn spheres and rational homology ball symplectic fillings

Alberto Cavallo, Antonio Alfieri, Irena Matkovi\v{c}

Brieskorn spheres admit no rational homology ball symplectic fillings for their contact structures except in listed cases.

arxiv:2605.13812 v1 · 2026-05-13 · math.GT · math.SG

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Claims

C1strongest claim

we obstruct the existence of rational homology ball symplectic fillings for any contact structure on −Y if n=3, and when there is no half convex Giroux torsion for n>3. Furthermore, we show that the same result holds for the Milnor fillable structure on Y with the possible exception of Σ(3,4,5), Σ(2,5,7) and Σ(2,3,6k+1) for k≥1. Along the way, we determine every canonically oriented Brieskorn sphere with vanishing correction term carrying at most two fillable structures, up to isotopy.

C2weakest assumption

The canonical orientation on the Brieskorn sphere Y and the precise definition of half-convex Giroux torsion are assumed to hold in the stated cases; the obstruction relies on the correction term vanishing or the absence of torsion without additional verification for all contact structures.

C3one line summary

Brieskorn spheres Σ(a1,...,an) obstruct rational homology ball symplectic fillings for any contact structure on -Y when n=3 or without half convex Giroux torsion for n>3, with limited exceptions for Milnor fillable cases, and those with vanishing correction terms have at most two fillable structures

References

28 extracted · 28 resolved · 2 Pith anchors

[1] P. Aceto, D. McCoy and J. H. Park,A survey on embeddings of3-manifolds in definite4-manifolds, arXiv:2407.03692

[2] S. Akbulut and K. Larson,Brieskorn spheres bounding rational balls, Proc. Am. Math. Soc.,146(2018), no. 4, pp. 1817–1824 2018

[3] A. Berman and R. Plemmons,Nonnegative matrices in the mathematical sciences, Volume 9 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994 1994

[4] M. Bhupal and A. Stipsicz,Weighted homogeneous singularities and rational homology disk smoothings, Am. J. Math.,133(2011), no. 5, pp. 1259–1297 2011

[5] Fillable structures on negative-definite Seifert fibred spaces · arXiv:2604.28174

Formal links

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Cited by

2 papers in Pith

Brieskorn spheres with two fillable contact structures

Mazur manifolds and symplectic structures

Receipt and verification

First computed	2026-05-18T02:44:15.384883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63797788a909fc9fc220ec0a59fa49d4e70a83f75b4f9fd8d22dc0ff2c585848

Aliases

arxiv: 2605.13812 · arxiv_version: 2605.13812v1 · doi: 10.48550/arxiv.2605.13812 · pith_short_12: MN4XPCFJBH6J · pith_short_16: MN4XPCFJBH6J7QRA · pith_short_8: MN4XPCFJ

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/MN4XPCFJBH6J7QRA5QFFT6SJ2T \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 63797788a909fc9fc220ec0a59fa49d4e70a83f75b4f9fd8d22dc0ff2c585848

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "bc8b2cd1021f69da1e248356e9bfcf07ae7c953b096bccc6e028acc8fe60f16c",
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      "math.SG"
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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-13T17:39:50Z",
    "title_canon_sha256": "6e333c9460e47fa126c1ef0f0de3255f8d218ae24021d4cd1430c9e7e53fc171"
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  "source": {
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    "kind": "arxiv",
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