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<p>For any object <i>A</i> in a simplicial model category <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_362_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {M}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">M</mi> </math></EquationSource> </InlineEquation>, we construct a topological space <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_362_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hat{A}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </math></EquationSource> </InlineEquation> which classifies homogeneous functors whose value on <i>k</i> open balls is equivalent to <i>A</i>. This extends a classification result of Weiss for homogeneous functors into topological spaces.</p>

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Classification of homogeneous functors in manifold calculus

  • 期刊论文

  • 发表日期：

    2025年2月6日

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  • Paul Arnaud Songhafouo Tsopméné,
  • Donald Stanley

摘要

For any object A in a simplicial model category \(\mathcal {M}\) M , we construct a topological space \(\hat{A}\) A ^ which classifies homogeneous functors whose value on k open balls is equivalent to A. This extends a classification result of Weiss for homogeneous functors into topological spaces.