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Linear representations of 3-manifold groups over rings


Authors: Stefan Friedl, Montek Gill and Stephan Tillmann
Journal: Proc. Amer. Math. Soc. 146 (2018), 4951-4966
MSC (2010): Primary 57M27, 57M50
DOI: https://doi.org/10.1090/proc/13984
Published electronically: August 10, 2018
MathSciNet review: 3856161
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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 $ \textup {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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Additional Information

Stefan Friedl
Affiliation: Universität Regensburg, Fakultät für Mathematik, 93053 Regensburg, Germany
Email: sfriedl@gmail.com

Montek Gill
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043
Email: montekg@umich.edu

Stephan Tillmann
Affiliation: School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia
Email: stephan.tillmann@sydney.edu.au

DOI: https://doi.org/10.1090/proc/13984
Received by editor(s): March 21, 2017
Received by editor(s) in revised form: September 18, 2017
Published electronically: August 10, 2018
Additional Notes: The first author was partially supported by SFB 1085 “Higher invariants” at the University of Regensburg, funded by the Deutsche Forschungsgemeinschaft (DFG)
The third author was partially supported by Australian Research Council grant DP140100158
Communicated by: David Futer
Article copyright: © Copyright 2018 American Mathematical Society