Geometry and Topology of Wild Translation Surfaces

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A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related.This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.