On the ends of groups and the Veech groups of infinite-genus surfaces

In this paper, we study the PSV construction, which provides a step by step method for obtaining tame translation surfaces with a suitable Veech group. In addition, we slightly modify this construction, and for each finitely generated subgroup G < GL+(2, R) without contracting elements, we produce a tame translation surface S with infinite genus such that its Veech group is G. Furthermore, the ends space of S can be written as B ⊔ U, where B is homeomorphic to the ends space of the gr