Local obstructions to asphericity of genus-one differential strata
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Are strata of genus-one differentials aspherical, meaning orbifold K(π,1) spaces with no higher homotopy? The local target studies arrangement obstructions that feed into non-asphericity of components with at least four zeros or poles.
Why it matters and what counts as progress
Why it matters: Local arrangement topology supplies obstructions to asphericity; an alternative local proof must remain distinct from the global transfer theorem.
What counts as progress: Prove the local obstructions by an independent route or establish their transfer to additional differential strata; a local lemma alone is not the global theorem.
How the problem developed
- 1997 · Conjecture [1]
Anton Zorich, recording a problem attributed to Maxim Kontsevich Recorded the question whether strata of Abelian and quadratic differentials are K(π,1) spaces, a problem later targeted by genus-one counterexamples.
- 23 Jun 2026 · Counterexamples [2]
Dawei Chen, Jingyin Huang, Yu Qiu and Fei Yu Claimed that every connected component of a genus-one differential stratum with at least four zeros or poles is not an orbifold K(π,1), giving infinitely many quadratic-differential counterexamples to the attributed conjecture.
- 23 Jun 2026 · Local argument [2]
Dawei Chen, Jingyin Huang, Yu Qiu and Fei Yu Included a local arrangement argument in an appendix that the authors say was first developed with AI and then verified by them; the global theorem is separately proved in the main text.
AI contribution
Non-asphericity of strata of genus-one differentials and stability spaces
Appendix A gives a Yoshinaga half-space-criterion proof of the two local arrangement obstructions used in genus-one differential-strata non-asphericity.
Sources
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Publication dates and editorial changes.
ChatGPT-assisted proof gives a second local obstruction argument