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<p>We prove that the Kontsevich graph complex <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textsf{GC}_d^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="sans-serif">GC</mi> <mi>d</mi> <mn>2</mn> </msubsup> </math></EquationSource> </InlineEquation> and its oriented version <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textsf{OGC}_{d+1}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="sans-serif">OGC</mi> <mrow> <mi>d</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> </math></EquationSource> </InlineEquation> are quasi-isomorphic as dg Lie algebras.</p>

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The oriented graph complex revisited

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Sergei Merkulov,
  • Thomas Willwacher,
  • Vincent Wolff

摘要

We prove that the Kontsevich graph complex \(\textsf{GC}_d^{2}\) GC d 2 and its oriented version \(\textsf{OGC}_{d+1}^2\) OGC d + 1 2 are quasi-isomorphic as dg Lie algebras.