Kontsevich's Asphericity Conjecture for Strata of Differentials
A conjecture attributed to Kontsevich holds that strata of quadratic differentials are aspherical, that is orbifold spaces. False: when there are at least four zeros or poles, no connected component of a genus-one stratum is an orbifold , giving infinitely many counterexamples, along with counterexamples for associated stability spaces.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Teichmuller theory
- Posed by
- Maxim Kontsevich
- Year posed
- —
- Years open
- —
- Solved
- 2026-06-23
- Model
- ChatGPT 5.5 Plus
- Vendor
- OpenAI
- Collaborators
- Dawei Chen, Jingyin Huang, Yu Qiu, Fei Yu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The authors state that the criterion in Appendix A arose first from an iterative, guided conversation with ChatGPT 5.5 Plus, and that they then verified, corrected and revised the proof.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2606.24135 - Non-asphericity of strata of genus-one differentials and stability spaces