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Limits of invariants of translation surfaces

A translation surface is a connected surface with a translation structure. For translation surfaces of finite type, there exists a rich theory, for example on moduli spaces of finite translation surfaces.

The goal of this project is to approach the definition of a good topology on the space of all
translation surfaces by a detour. Instead of studying the space itself, we study four types of invariants
that are living in spaces which are better understood:

  • geometric invariants such as Cheeger constants or systoles,
  • Siegel-Veech constants,
  • Veech groups, and
  • saddle connection complexes.

Publications


    Team Members

    Dr. Anja Randecker
    Project leader
    Ruprecht-Karls-Universität Heidelberg
    randecker(at)mathi.uni-heidelberg.de

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