Pith Number

pith:U4W4GUTV

pith:2026:U4W4GUTVNC3D3B3KV2JQJNW5AL

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Boundary Dehn twists are often commutators

Ayodeji Lindblad

Boundary Dehn twists on punctured 4-manifolds are commutators of two diffeomorphisms

arxiv:2604.13194 v2 · 2026-04-14 · math.GT

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Claims

C1strongest claim

For X any complete intersection of even complex dimension or any connected sum thereof (or, more generally, any space among certain broad classes of smooth manifolds), we concretely construct orientation-preserving diffeomorphisms a,c of punctured X rel boundary whose commutator [a,c] represents the smooth mapping class rel boundary of the boundary Dehn twist.

C2weakest assumption

The explicit constructions of diffeomorphisms a and c exist and satisfy the commutator relation for the stated broad classes of smooth 4-manifolds, and that the boundary Dehn twist is indeed the image of this commutator in the mapping class group rel boundary.

C3one line summary

Boundary Dehn twists on punctured even-dimensional complete intersections and connected sums are commutators in the smooth mapping class group rel boundary, hence trivial after abelianization.

Cited by

1 paper in Pith

Diffeomorphism groups and gauge theory for families

Receipt and verification

First computed	2026-05-29T01:04:37.420404Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a72dc3527568b63d876aae9304b6dd02f55efd5aed00919aaddb550d36a1b5c7

Aliases

arxiv: 2604.13194 · arxiv_version: 2604.13194v2 · doi: 10.48550/arxiv.2604.13194 · pith_short_12: U4W4GUTVNC3D · pith_short_16: U4W4GUTVNC3D3B3K · pith_short_8: U4W4GUTV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/U4W4GUTVNC3D3B3KV2JQJNW5AL \
  | 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: a72dc3527568b63d876aae9304b6dd02f55efd5aed00919aaddb550d36a1b5c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf8e6a9fa34ce37cd084c93191e8b120f0f541352a76d4634972a58213849ab8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-04-14T18:17:03Z",
    "title_canon_sha256": "556ebfbea89ca4ca2ad68e1178d0931a91eaf4b478b0ad0bfbe743816b75a8d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.13194",
    "kind": "arxiv",
    "version": 2
  }
}