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<p>In this paper we prove that all the homology groups of the real nerve of the moduli space of Riemann surfaces of even genus <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(g&gt;4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>&gt;</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> are nontrivial. The crucial role in our constructions comes from the information known about the Riemann surfaces admitting the maximal number of symmetries and the ones admitting the maximal numbers of ovals.</p>

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All the homology groups of the real nerve of the moduli space of Riemann surfaces of even genera \(g>4\) are nontrivial

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • Ewa Kozłowska-Walania

摘要

In this paper we prove that all the homology groups of the real nerve of the moduli space of Riemann surfaces of even genus \(g>4\) g > 4 are nontrivial. The crucial role in our constructions comes from the information known about the Riemann surfaces admitting the maximal number of symmetries and the ones admitting the maximal numbers of ovals.