Simple loop conjecture for discrete representations in PSL$(2,\,\mathbb R)$

Gianluca Faraco; Subhojoy Gupta

Simple loop conjecture for discrete representations in PSL$(2,\,\mathbb R)$

Geometric Topology 2025-06-18 v2

Authors: Gianluca Faraco , Subhojoy Gupta

Abstract

We show that the Simple Loop Conjecture holds for any representation $\rho\colon\pi_1(S)\longrightarrow \text{PSL}(2,\,\mathbb R)$ that is discrete but not faithful. That is, we show the existence of a simple closed curve in the kernel of such a representation.

Keywords

conjectures and proofs

Cite

@article{arxiv.2307.12066,
  title  = {Simple loop conjecture for discrete representations in PSL$(2,\,\mathbb R)$},
  author = {Gianluca Faraco and Subhojoy Gupta},
  journal= {arXiv preprint arXiv:2307.12066},
  year   = {2025}
}

Comments

We have decided to withdraw this paper due to a mistake in the main result. A counterexample to the principal theorem has come to our attention, invalidating the statement as originally formulated. We hope to upload a corrected version in the future

Simple loop conjecture for discrete representations in PSL$(2,\,\mathbb R)$

Abstract

Keywords

Cite

Comments

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