2025/03/24 by Hidalgo, Ruben A.
#14H37 #14H55 #30F10 #30F20 #32G15 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2503.19080
The Loch Ness monster (LNM) is, up to homeomorphisms, the unique orientable, connected, Hausdorff, second countable surface of infinite genus and with exactly one end. For each integer k ≥ 2, we construct Riemann surface structures S on the LNM admitting a group of conformal automorphisms H ≅ \mathbb Zk\mathbb N such that S/H is planar. These structures can be described algebraically inside the projective space \mathbb P\mathbb N after deleting some limit points.