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<p>In this paper, we introduce a new regularity condition that characterizes the tameness of a composite singularity <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H=G\circ F\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo>=</mo> <mi>G</mi> <mo>∘</mo> <mi>F</mi> </mrow> </math></EquationSource> </InlineEquation> in a sharp way. Our approach will provide a natural tool to study the topology of composite singularities <i>H</i> by relating the singular sets and Milnor sets of the component map germs <i>F</i> and <i>G</i> to those of <i>H</i>. We also study the invariance of tameness by <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {L}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">L</mi> </math></EquationSource> </InlineEquation>-equivalence, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">R</mi> </math></EquationSource> </InlineEquation>-equivalence, and hence by <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {A}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">A</mi> </math></EquationSource> </InlineEquation>-equivalence.</p>

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Tameness conditions for composite singularities

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月26日

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  • R. Araújo dos Santos,
  • D. Dreibelbis,
  • M. Ribeiro,
  • I. Santamaria Guarín

摘要

In this paper, we introduce a new regularity condition that characterizes the tameness of a composite singularity \(H=G\circ F\) H = G ∘ F in a sharp way. Our approach will provide a natural tool to study the topology of composite singularities H by relating the singular sets and Milnor sets of the component map germs F and G to those of H. We also study the invariance of tameness by \(\mathcal {L}\) L -equivalence, \(\mathcal {R}\) R -equivalence, and hence by \(\mathcal {A}\) A -equivalence.