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<p>We study the higher (or sequential) topological complexity <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\operatorname {TC}_s\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mo>TC</mo> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation> of manifolds with abelian fundamental group. We give sufficient conditions for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\operatorname {TC}_s\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mo>TC</mo> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation> to be non-maximal in both the orientable and non-orientable cases. In combination with cohomological lower bounds, we also obtain some exact values for certain families of manifolds.</p>

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On the higher topological complexity of manifolds with abelian fundamental group

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月26日

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  • N. Cadavid-Aguilar,
  • D. Cohen,
  • J. González,
  • S. Hughes,
  • L. Vandembroucq

摘要

We study the higher (or sequential) topological complexity \(\operatorname {TC}_s\) TC s of manifolds with abelian fundamental group. We give sufficient conditions for \(\operatorname {TC}_s\) TC s to be non-maximal in both the orientable and non-orientable cases. In combination with cohomological lower bounds, we also obtain some exact values for certain families of manifolds.