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<p>Apisa-Wright conjectured that all branched covers of quadratic differentials in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {Q}(-1^4)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">Q</mi> <mo stretchy="false">(</mo> <mo>-</mo> <msup> <mn>1</mn> <mn>4</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with at most one cylinder in each direction are cyclic covers. We provide infinitely many counterexamples to this conjecture.</p>

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An infinite family of non-cyclic 1-cylinder pillowcase-tiled surfaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月26日

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  • Malak Abdalla,
  • Gabriela Brown

摘要

Apisa-Wright conjectured that all branched covers of quadratic differentials in \(\mathcal {Q}(-1^4)\) Q ( - 1 4 ) with at most one cylinder in each direction are cyclic covers. We provide infinitely many counterexamples to this conjecture.