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Kontsevich's Asphericity Conjecture for Strata of Differentials

Geometry & topology · posed by Maxim Kontsevich · disproved

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Statement

A conjecture attributed to Kontsevich holds that strata of quadratic differentials are aspherical, that is orbifold K(π,1)K(\pi,1) spaces. False: when there are at least four zeros or poles, no connected component of a genus-one stratum is an orbifold K(π,1)K(\pi,1), giving infinitely many counterexamples, along with counterexamples for associated stability spaces.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Dawei Chen, Jingyin Huang, Yu Qiu and Fei Yu, using ChatGPT 5.5 Plus

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    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.

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