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<p>We reprove the generalized Nandakumar–Ramana Rao conjecture for the prime case using representation ring-graded Bredon cohomology. Our approach relies solely on the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_383_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\(RO(C_p)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>O</mi> <mo stretchy="false">(</mo> <msub> <mi>C</mi> <mi>p</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-graded cohomology of configuration spaces, viewed as a module over the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_383_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\(RO(C_p)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>O</mi> <mo stretchy="false">(</mo> <msub> <mi>C</mi> <mi>p</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-graded Bredon cohomology of a point.</p>

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Revisiting the Nandakumar–Ramana Rao conjecture

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • Surojit Ghosh,
  • Ankit Kumar

摘要

We reprove the generalized Nandakumar–Ramana Rao conjecture for the prime case using representation ring-graded Bredon cohomology. Our approach relies solely on the \(RO(C_p)\) R O ( C p ) -graded cohomology of configuration spaces, viewed as a module over the \(RO(C_p)\) R O ( C p ) -graded Bredon cohomology of a point.