Pith Number

pith:YMTZ54L3

pith:2026:YMTZ54L3OM5FQMTIQAHXVQLH6M

not attested not anchored not stored refs resolved

Mazur manifolds and symplectic structures

Alberto Cavallo

Heegaard Floer cobordism maps obstruct symplectic structures on specific Akbulut-Kirby Mazur manifolds bounded by Brieskorn spheres.

arxiv:2605.15095 v1 · 2026-05-14 · math.GT · math.SG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YMTZ54L3OM5FQMTIQAHXVQLH6M}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We use the Heegaard Floer homology cobordism maps to obstruct the existence of a symplectic structure on the Akbulut-Kirby Mazur manifolds whose boundary is a Brieskorn sphere Y among Σ(2,3,13), Σ(2,5,7) and Σ(3,4,5).

C2weakest assumption

The Heegaard Floer cobordism maps for the specific 2-handles and the chosen Brieskorn spheres detect the absence of a symplectic structure without additional assumptions on the filling or on the contact structure induced on the boundary.

C3one line summary

Mazur manifolds with boundaries Σ(2,3,13), Σ(2,5,7), and Σ(3,4,5) admit no symplectic structure, producing exotic pairs of simply connected 4-manifolds with definite intersection forms.

References

24 extracted · 24 resolved · 2 Pith anchors

[1] S. Akbulut,Cork twists and automorphisms of3-manifolds, J. Gökova Geom. Topol. GGT.,14(2020), pp. 1–13 2020

[2] S. Akbulut and S. Durusoy,An involution acting nontrivially on Heegaard-Floer homology, Geometry and topology of manifolds. Papers from the conference held at McMaster University, Hamilton, ON, Canada 2004

[3] S. Akbulut and Ç. Karakurt,Action of the Cork twist on Floer homology, Proceedings of the 18th Gökova geometry-topology conference, Gökova, Turkey, May 30–June 4, 2011 2011

[4] S. Akbulut and R. Kirby,Mazur manifolds, Michigan Math. J.,26(1979), no. 3, pp. 259–284 1979

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

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T21:40:25.870269Z
Last reissued	2026-05-17T21:57:19.197182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

c3279ef17b733a583268800f7ac167f3202465222238a4a358b49acd36fcc3fa

Aliases

arxiv: 2605.15095 · arxiv_version: 2605.15095v1 · pith_short_12: YMTZ54L3OM5F · pith_short_16: YMTZ54L3OM5FQMTI · pith_short_8: YMTZ54L3

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YMTZ54L3OM5FQMTIQAHXVQLH6M \
  | 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: c3279ef17b733a583268800f7ac167f3202465222238a4a358b49acd36fcc3fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24d31e18247bd05c5b57e42da8ae15fc3ccc146f4ad23a98fb85fb159b52c781",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-14T17:14:03Z",
    "title_canon_sha256": "5b46d38909a2bd6ddbaf7549428f98a6e026f9f31791ba86ab4a157f5ee2bfb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15095",
    "kind": "arxiv",
    "version": 1
  }
}