Linear representations of 3–manifold groups over rings
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- by Stefan Friedl, Montek Gill and Stephan Tillmann PDF
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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 $\mathrm {PGL}_2(R),$ 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.References
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Additional Information
- Stefan Friedl
- Affiliation: Universität Regensburg, Fakultät für Mathematik, 93053 Regensburg, Germany
- MR Author ID: 746949
- 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
- MR Author ID: 663011
- ORCID: 0000-0001-6731-0327
- Email: stephan.tillmann@sydney.edu.au
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4951-4966
- MSC (2010): Primary 57M27, 57M50
- DOI: https://doi.org/10.1090/proc/13984
- MathSciNet review: 3856161