Year: 2026
Type: preprint
Abstract: This paper studies Veech groups of dilation surfaces whose fundamental group is not finitely generated. We prove that if $ S$ is a surface with self-similar end space and every end is accumulated by genus, then every countable subgroup of $SL(2,\mathbb{R}) $ can be realized as the Veech group of a dilation surface homeomorphic to $ S$. Additionally, we can construct this dilation surface such that it realizes horizon saddle connections in a prescribed set of directions. This contrasts with the case of closed dilation surfaces, where horizon saddle connections impose restrictions on the algebraic structure of the Veech group.
Source: arXiv (Cornell University)
Author: Medrano, Oscar Rutilio Molina
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214617347