Linear representations of 3-manifold groups over rings

Stefan Friedl; Montek Gill; Stephan Tillmann

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arXiv · 1703.06609

Linear representations of 3-manifold groups over rings

Stefan Friedl·Montek Gill·Stephan Tillmann

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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 $PGL(2,R),$ 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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Stefan Friedl, Montek Gill, Stephan Tillmann. 2017-03-20. Linear representations of 3-manifold groups over rings. https://arxiv.org/abs/1703.06609

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