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Linear representations of 3–manifold groups over rings

Friedl, Stefan ; Gill, Montek ; Tillmann, Stephan


The fundamental groups of compact 3-manifolds are known to be residually finite. Feng Luo conjectured that a stronger statement is true, by only allowing finite groups of the form PGL(2)(R), where R is some finite commutative ring with identity. We give an equivalent formulation of Luo's conjecture via faithful representations and provide various examples and a counterexample.

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