科研之友
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摘要
In this note, we give an explicit counterexample to the simple loop conjecture for representations of surface groups into PSL (2, R). Specifically, we use a construction of DeBlois and Kent to show that for any orientable surface with negative Euler characteristic and genus at least 1, there are uncountably many nonconjugate, noninjective 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.
- 出版日期2014-6
