PreprintCC BY 4.0arXiv
The Torelli Group and Euler Class Zero PSL(2,ℝ) Representations
Abstract
We prove that every representation of a closed surface group of genus at least $3$ into PSL(2,ℝ) that is sufficiently close (but not equal to) a representation that has non-compact solvable image has a simple closed separating curve that is mapped to a non-trivial elliptic element in PSL(2,ℝ). This can be seen as evidence for an affirmative answer to a question of Bowditch and a conjecture of Goldman.
Related
- Quilt decompositions of surfaces and Torelli group action on the extended Hatcher complex
- Modular fusion categories with trivial Torelli group actions
- Global Existence and Scattering of a Class of Two-Dimensional Euler--Poisson--Korteweg Systems
- A well-posedness theory for the 2D inhomogeneous incompressible Euler equations and a class of global-in-time solutions
- Rigidity of stationary and uniformly rotating planar Euler flows in the C1 Yudovich class
BibTeX
@misc{bobb2026torelli,
title = {{The Torelli Group and Euler Class Zero $\mathrmPSL(2,\mathbbR)$ Representations}},
author = {Marit Bobb and James Farre and Peter Smillie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40040},
eprint = {2610.40040},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40040},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Torelli Group and Euler Class Zero PSL(2,ℝ) Representations
AU - Marit Bobb
AU - James Farre
AU - Peter Smillie
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40040
UR - https://arxiv.org/abs/2610.40040
AB - We prove that every representation of a closed surface group of genus at least $3$ into PSL(2,ℝ) that is sufficiently close (but not equal to) a representation that has non-compact solvable image has a simple closed separating curve that is mapped to a non-trivial elliptic element in PSL(2,ℝ). This can be seen as evidence for an affirmative answer to a question of Bowditch and a conjecture of Goldman.
ER -