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Kontsevich's Asphericity Conjecture for Strata of Differentials

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kontsevich-strata-asphericityGeometry & topologyposed by Maxim Kontsevichrecorded: disproved

1 attempt · no person has looked

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.

Context

An asphericity conjecture attributed to Kontsevich about strata of differentials, standard background in Teichmuller dynamics and stability conditions.

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  • #1

    Attempt 1

    proof attemptChatGPT 5.5 Plus with Dawei Chen, Jingyin Huang, Yu Qiu, Fei Yu ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    ChatGPT 5.5 Plus
    people
    Dawei Chen, Jingyin Huang, Yu Qiu, Fei Yu

    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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