Open Research Index

Taming implies compatibility on four-manifolds

OpenAI

OpenAI Mathopenai-math/Taming-implies-compatibility-on-four-manifoldsOct 6, 2026math.DGAI-generatedscore 0

We prove that every smooth almost complex structure on a closed four-manifold which is tamed by a symplectic form is compatible with a symplectic form. This gives a positive solution to Donaldson's tamed-to-compatible conjecture. We also characterize the compatible cone by strict intersection positivity on the closure of the invariant part of the taming cone.

SourcePDFJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/openai-math/Taming-implies-compatibility-on-four-manifolds
curl -X POST /api/v1/records/openai-math/Taming-implies-compatibility-on-four-manifolds/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/Taming-implies-compatibility-on-four-manifolds/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'