The Torelli Group and Euler Class Zero $\mathrm{PSL}(2,\mathbb{R})$ Representations

Marit Bobb; James Farre; Peter Smillie

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arXiv · 2610.40040

The Torelli Group and Euler Class Zero $\mathrm{PSL}(2,\mathbb{R})$ Representations

Marit Bobb·James Farre·Peter Smillie

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Abstract

We prove that every representation of a closed surface group of genus at least $3$ into $\mathrm{PSL}(2,\mathbb{R})$ 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 $\mathrm{PSL}(2,\mathbb{R})$. This can be seen as evidence for an affirmative answer to a question of Bowditch and a conjecture of Goldman.

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Marit Bobb, James Farre, Peter Smillie. 2026-10-29. The Torelli Group and Euler Class Zero $\mathrm{PSL}(2,\mathbb{R})$ Representations. https://arxiv.org/abs/2610.40040

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