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<p>Let <i>K</i> be a finite simplicial complex, let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(g:K\rightarrow K\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>:</mo> <mi>K</mi> <mo stretchy="false">→</mo> <mi>K</mi> </mrow> </math></EquationSource> </InlineEquation> be a simplicial map and let <i>f</i> be a discrete Morse–Bott function on <i>K</i> satisfying <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f(g(\sigma ))\le f(\sigma )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>σ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>≤</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>σ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for all simplices <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation> in <i>K</i>. We establish a set of inequalities (generalizing the Morse–Bott inequalities which we recover as a particular case when <i>g</i> is the identity) relating the dynamics of <i>g</i> and <i>f</i>.</p>

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Morse–Bott inequalities for endomorphisms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月11日

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  • Enrique Macías-Virgós,
  • Alejandro O. Majadas-Moure,
  • David Mosquera-Lois,
  • José Antonio Vilches

摘要

Let K be a finite simplicial complex, let \(g:K\rightarrow K\) g : K → K be a simplicial map and let f be a discrete Morse–Bott function on K satisfying \(f(g(\sigma ))\le f(\sigma )\) f ( g ( σ ) ) ≤ f ( σ ) for all simplices \(\sigma \) σ in K. We establish a set of inequalities (generalizing the Morse–Bott inequalities which we recover as a particular case when g is the identity) relating the dynamics of g and f.