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<p>In this paper, we prove an upper bound on the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\widehat{A}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </math></EquationSource> </InlineEquation> genus of a smooth, closed, spin Riemannian manifold in terms of the scalar curvature lower bound, volume and Neumann isoperimetric constant. Moreover, we construct an example to show that the Neumann isoperimetric constant in this bound is necessary. Our result partially answers a question of Gromov on bounding characteristic numbers using scalar curvature lower bound.</p>

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Bounding the A-hat Genus Using Scalar Curvature Lower Bounds and Isoperimetric Constants

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Qiaochu Ma,
  • Jinmin Wang,
  • Guoliang Yu,
  • Bo Zhu

摘要

In this paper, we prove an upper bound on the \(\widehat{A}\) A ^ genus of a smooth, closed, spin Riemannian manifold in terms of the scalar curvature lower bound, volume and Neumann isoperimetric constant. Moreover, we construct an example to show that the Neumann isoperimetric constant in this bound is necessary. Our result partially answers a question of Gromov on bounding characteristic numbers using scalar curvature lower bound.