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- W3100134821 abstract "In this note, we give an explicit counterexample to the simple loop conjecture for representations of surface groups into PSL(2,R). Specifically, we show that for any surface with negative Euler characteristic and genus at least 1, there are uncountably many non-conjugate, non-injective homomorphisms of its fundamental group into PSL(2,R) that kill no simple closed curve (nor any power of a simple closed curve). This result is not new -- work of Louder and Calegari for representations of surface groups into SL(2, C) applies to the PSL(2,R) case, but our approach here is explicit and elementary." @default.
- W3100134821 created "2020-11-23" @default.
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- W3100134821 date "2014-07-26" @default.
- W3100134821 modified "2023-10-17" @default.
- W3100134821 title "A counterexample to the simple loop conjecture for PSL(2,ℝ)" @default.
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- W3100134821 doi "https://doi.org/10.2140/pjm.2014.269.425" @default.
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