title: Geometric Invariants and Asymptotics of Translation Surfaces
creator: Reichert, Maurice
subject: ddc-510
subject: 510 Mathematics
description: By gluing together polygons along parallel edges in a well-defined matter, we obtain translation surfaces, which are two-dimensional manifolds with rich geometric structures.    This thesis examines the geometry of translation surfaces with a focus on understanding the properties of random translation surfaces of high genus in order to gain a broader understanding of the moduli space of translation surfaces.     One of the primary challenges in this field is bridging the gap between finite and infinite translation surfaces corresponding to the compact and non-compact cases.  We address this challenge by examining the convergence of sequences of finite translation surfaces from different strata and approximating infinite translation surfaces with them.    We use different methods to achieve this approximation. On the one hand, we use some sense of convergence in the underlying Veech group to approach infinite translation surfaces; on the other hand, we want to understand geometric invariants for translation surfaces of large genus. In particular, we explore the behavior of the Cheeger constant, a measure of the inverse of bottleneckedness.    By advancing existing constructions, introducing new perspectives, and analyzing key geometric invariants, this thesis enhances our understanding of translation surfaces for future research.
date: 2024
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserver/35709/1/Geometric%20Invariants%20and%20Asymptotics%20of%20Translation%20Surfaces.pdf
identifier: DOI:10.11588/heidok.00035709
identifier: urn:nbn:de:bsz:16-heidok-357099
identifier:   Reichert, Maurice  (2024) Geometric Invariants and Asymptotics of Translation Surfaces.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/35709/
rights: info:eu-repo/semantics/openAccess
rights: Please see front page of the work (Sorry, Dublin Core plugin does not recognise license id)
language: eng