Pith Number

pith:G3UCCPO4

pith:2026:G3UCCPO4CNUOKOA7XKKTETP26L

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Bulk-deformations, Floer complex bordism, and Grothendieck-Riemann-Roch

Kenneth Blakey, Noah Porcelli

For Liouville manifolds the complexified lift of symplectic cohomology to complex cobordism equals the version bulk-deformed by the Chern character.

arxiv:2605.06620 v2 · 2026-05-07 · math.SG · math.AG · math.AT

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Claims

C1strongest claim

Given a Liouville manifold, we compute a Floer-homotopical invariant -- the complexification of the lift of symplectic cohomology to complex cobordism -- in terms of a classical Floer-theoretic invariant, namely, symplectic cohomology bulk-deformed by the Chern character.

C2weakest assumption

That an explicit model exists for the complexified homotopy groups of the MU-module spectrum associated to a complex-oriented flow category, and that a homotopy-coherent version of the Grothendieck-Riemann-Roch theorem holds for this model (as invoked in the abstract to establish the main computation).

C3one line summary

Establishes relation between MU-lifted symplectic cohomology and bulk-deformed version via homotopy coherent GRR, yielding computable criterion for non-trivial complex cobordism classes.

References

16 extracted · 16 resolved · 5 Pith anchors

[1] Foundation of Floer homotopy theory I: flow categories

[2] Symplectic cohomology and viterbo’s theorem.arXiv preprint arXiv:1312.3354 · arXiv:1312.3354

[3] On arborealization, Maslov data, and lack thereof

[4] [BB25] Kenneth Blakey and Ciprian M. Bonciocat. Parametrized Lagrangian Floer homotopy. arXiv:2601.08506,

[5] [Bla] Kenneth Blakey 1992

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:00:41.107730Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36e8213ddc1368e5381fba95324dfaf2e0a8a8a13d2ba5519667efd4b7808e3f

Aliases

arxiv: 2605.06620 · arxiv_version: 2605.06620v2 · doi: 10.48550/arxiv.2605.06620 · pith_short_12: G3UCCPO4CNUO · pith_short_16: G3UCCPO4CNUOKOA7 · pith_short_8: G3UCCPO4

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/G3UCCPO4CNUOKOA7XKKTETP26L \
  | 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: 36e8213ddc1368e5381fba95324dfaf2e0a8a8a13d2ba5519667efd4b7808e3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3cba9943ecf3918987c6994bf2676552c2a83e501e6a15ebe8eebf4029d8b365",
    "cross_cats_sorted": [
      "math.AG",
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2026-05-07T17:34:40Z",
    "title_canon_sha256": "468f27a5d156a5cd662bd726cd35da4629ea407040e4411385d43fb2bc51cf8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.06620",
    "kind": "arxiv",
    "version": 2
  }
}