Repositorio
Institucional

Hidalgo, Ruben A.

HOMOLOGY GROUP AUTOMORPHISMS OF RIEMANN SURFACES

INDEPENDENT UNIV MOSCOW-IUM

MOSCOW MATHEMATICAL JOURNAL

en

If & UGamma, is a finitely generated Fuchsian group such that its derived subgroup & UGamma,' is co-compact and torsion free, then S =H2/& UGamma,' is a closed Riemann surface of genus g ?, 2 admitting the abelian group A = & UGamma,/& UGamma,' as a group of conformal automorphisms. We say that A is a homology group of S. A natural question is if S admits unique homology groups or not, in other words, if there are different Fuchsian groups & UGamma,1 and & UGamma,2 with & UGamma,'1 = & UGamma,'2? It is known that if & UGamma,1 and & UGamma,2 are both of the same signature (0, k, ... , k), for some k ?, 2, then the equality & UGamma,'1 = & UGamma,'2 ensures that & UGamma,1 = & UGamma,2. Generalizing this, we observe that if & UGamma,j has signature (0, kj, ..., kj) and & UGamma,'1 = & UGamma,'2, then & UGamma,1 = & UGamma,2. We also provide examples of surfaces S with different homology groups. A description of the normalizer in Aut(S) of each homology group A is also obtained.

2023

artículo original

10.17323/1609-4514-2023-23-1-113-120

PDF

Riemann surface

automorphism

Fuchsian group

Matemáticas

superficie de Riemann

automorfismo

grupo fucsia

113.0

120

artículo original

versión publicada

metadata

https://arxiv.org/abs/2007.01778

metadata

WOS:001052659800006

1609-3321

verde

Matemáticas

ANID FONDECYT 1190001

ANID FONDECYT 1220261