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The Thurston spine and equivariant cell decompositions in genus 2

  • Ni An
  • Jiexing Chen
  • Ingrid Irmer
  • Paul Schmutz Schaller
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Abstract

The Thurston spine of the genus 2 Teichmüller space of closed compact surfaces is obtained. In particular, we identify all mapping class group-orbits of filling sets of systoles in genus 2. Thereby, surprisingly rich cases already appear in this simplest case which is genus 2. This is contrasted with a cell decomposition of a bordification of Teichmüller space obtained computationally using Rivin's angle coordinates, on which the cells are labelled by Delaunay graphs closely related to our systolic graphs.

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Cite

BibTeXRIS
BibTeX
@misc{an2026thurston,
  title = {{The Thurston spine and equivariant cell decompositions in genus 2}},
  author = {Ni An and Jiexing Chen and Ingrid Irmer and Paul Schmutz Schaller},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38254},
  eprint = {2609.38254},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38254},
}
RIS
TY  - UNPB
TI  - The Thurston spine and equivariant cell decompositions in genus 2
AU  - Ni An
AU  - Jiexing Chen
AU  - Ingrid Irmer
AU  - Paul Schmutz Schaller
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.38254
UR  - https://arxiv.org/abs/2609.38254
AB  - The Thurston spine of the genus 2 Teichmüller space of closed compact surfaces is obtained. In particular, we identify all mapping class group-orbits of filling sets of systoles in genus 2. Thereby, surprisingly rich cases already appear in this simplest case which is genus 2. This is contrasted with a cell decomposition of a bordification of Teichmüller space obtained computationally using Rivin's angle coordinates, on which the cells are labelled by Delaunay graphs closely related to our systolic graphs.
ER  -