2020/05/19 by Yasmina Atarihuana, Atarihuana, Yasmina, Juan Antonio Garcı́a +7
Mathematics · #14H37 #14H57 #20H10 #37F10 #57N05 #57N16 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2005.09804
openalex publication_date 2020/05/19 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The classical theory of dessin d'enfants, which are bipartite maps on compact\norientable surfaces, are combinatorial objects used to study branched covers\nbetween compact Riemann surfaces and the absolute Galois group of the field of\nrational numbers. In this paper, we show how this theory is naturally extended\nto non-compact orientable surfaces and, in particular, we observe that the Loch\nNess monster (the surface of infinite genus with exactly one end) admits\ninfinitely many regular dessins d'enfants (either chiral or reflexive). In\naddition, we study different holomorphic structures on the Loch Ness monster,\nwhich come from homology covers of compact Riemann surfaces, infinite\nhyperelliptic and infinite superelliptic curves.\n