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<p>We construct non-trivial elements in the homotopy groups of the observer moduli space of positive sectional curvature metrics on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {C}P^n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">C</mi> <msup> <mi>P</mi> <mi>n</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> and non-trivial elements in the homotopy groups of the observer moduli space of positive scalar curvature metrics on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {C}P^2 \sharp M^4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">C</mi> <msup> <mi>P</mi> <mn>2</mn> </msup> <mo>♯</mo> <msup> <mi>M</mi> <mn>4</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Moduli spaces of positive curvature metrics in dimension four and beyond

  • 期刊论文

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  • 发表日期：

    2026年2月11日

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  • Thorsten Hertl

摘要

We construct non-trivial elements in the homotopy groups of the observer moduli space of positive sectional curvature metrics on \(\mathbb {C}P^n\) C P n and non-trivial elements in the homotopy groups of the observer moduli space of positive scalar curvature metrics on \(\mathbb {C}P^2 \sharp M^4\) C P 2 ♯ M 4 .