Families of Infinite Translation Surfaces related to the Chamanara Surface

In his work from 2004 Reza Chamanara established a family of translation surfaces $Ch\alpha$ for $\alpha\in(0,1)$ , the so-called Chamanara surfaces. In this talk we will generalize this construction and have a look at some families consisting of these generalized surfaces. We will ask the question if there is some form of natural homeomorphism from these families to a suitable vector space. To answer this we will take a look at the strong immersive topology on the moduli space of all (finite and infinite) translation surfaces. This topology is slightly stronger than the immersive topology which was constructed by Patrick Hooper in 2013.