On the monodromies of strata of (half-)translation surfaces

Giannini, Riccardo (2025) On the monodromies of strata of (half-)translation surfaces. PhD thesis, University of Glasgow.

Abstract

The present work consists of two independent parts devoted to the study of topological monodromy maps of strata of (half-)translation surfaces. As the name suggests, topological monodromies provide some important topological data for such strata (Lemma 2.4.1), considered by many authors as the loci of fundamental dynamical actions. Inspired by Calderon–Salter’s description of the images of the topological monodromy maps of non-hyperelliptic strata of translation surfaces ([Cal20], [CS21] and [CS22]), we estimated the size of the respective kernels in low genera and in particular in the case of the non-hyperelliptic strata Hodd(4) and H(3, 1) in genus 3 and Heven(6) in genus 4. We prove that the kernel contains a non-abelian free group of rank 2. In the second part, we study the topological monodromy maps of strata of half-translation surfaces, a generalisation of the concept of translation surface. Here, we improve Walker’s result [Wal09] and provide a promising candidate for the image of the topological monodromies as subgroups of the mapping class groups.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Supervisor's Name: Brendle, Professor Tara and Gadre, Professor Vaibhav
• Date of Award: 2025
• Depositing User: Theses Team
• Unique ID: glathesis:2025-85499
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 03 Oct 2025 15:03
• Last Modified: 03 Oct 2025 15:05
• Thesis DOI: 10.5525/gla.thesis.85499
• URI: https://theses.gla.ac.uk/id/eprint/85499