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<p>Let <i>M</i> be a closed aspherical manifold. Assume that the rational strong Novikov conjecture holds for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\pi _1(M)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>π</mi> <mn>1</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. We show that on any spin surgery of <i>M</i> along a region whose induced homomorphism on the fundamental group is trivial, every complete metric with non-negative scalar curvature is Ricci-flat. In particular, on the connected sum of <i>M</i> with a spin manifold, any complete metric with non-negative scalar curvature is Ricci-flat.</p>

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Non-negative scalar curvature on spin surgeries and Novikov conjecture

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Jinmin Wang

摘要

Let M be a closed aspherical manifold. Assume that the rational strong Novikov conjecture holds for \(\pi _1(M)\) π 1 ( M ) . We show that on any spin surgery of M along a region whose induced homomorphism on the fundamental group is trivial, every complete metric with non-negative scalar curvature is Ricci-flat. In particular, on the connected sum of M with a spin manifold, any complete metric with non-negative scalar curvature is Ricci-flat.