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

Abstract

We show that the Simple Loop Conjecture holds for any representation $\ddot{I}:\ddot{I}{€}_1(S)⟶\text{PSL}(2,\mathbb{R})$ that is discrete but not faithful. That is, we show the existence of a simple closed curve in the kernel of such a representation.

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