Applying the Riemann surfaces with extremal configurations of symmetries to the study of the real nerve of the moduli space of Riemann surfaces of odd genera

Ewa Kozłowska-Walania; Leonard Sikorski

doi:10.56754/0719-0646.2802.295

DOI:

https://doi.org/10.56754/0719-0646.2802.295

Abstract

In this paper we find the necessary and sufficient conditions for the geometrical dimension of the real nerve of the moduli space of Riemann surfaces of odd genus \(g\) to be maximal. Furthermore, we prove some properties of Riemann surfaces with extremal configuration of symmetries which lead to the conclusion that certain homology groups of the real nerve \(\mathcal{N}_g\) of the moduli space of Riemann surfaces of odd genus \(g\) are nontrivial.

Keywords

Riemann surface , symmetry of a Riemann surface , real form , automorphisms of Riemann surface , Fuchsian groups , Riemann uniformization theorem , separating symmetry

Mathematics Subject Classification:

30F99 , 14H37 , 20F

Ewa Kozłowska-Walania Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland. https://orcid.org/0000-0001-5208-6318
Leonard Sikorski Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland. https://orcid.org/0000-0003-0797-4011

Pages: 295-321
Date Published: 2026-05-18
Vol. 28 No. 2 (2026)

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