Linear representations of 3–manifold groups over rings

Friedl, Stefan; Gill, Montek; Tillmann, Stephan

doi:10.1090/proc/13984

Linear representations of 3–manifold groups over rings
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by Stefan Friedl, Montek Gill and Stephan Tillmann PDF

Proc. Amer. Math. Soc. 146 (2018), 4951-4966 Request permission

Abstract:

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 $\mathrm {PGL}_2(R),$ 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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