The noncocompact \operatorname{SL}33 arithmetic-subgroup conjecture

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Let Γ\Gamma be a noncocompact arithmetic subgroup of either SL⁡(3,R)\operatorname{SL}(3,\mathbb{R}) or SL⁡(3,C)\operatorname{SL}(3,\mathbb{C}). A faithful action on R\mathbb{R} means an action with trivial kernel. The noncocompact SL⁡(3)\operatorname{SL}(3) conjecture. Noncocompact arithmetic subgroups of SL⁡(3,R)\operatorname{SL}(3,\mathbb{R}) and SL⁡(3,C)\operatorname{SL}(3,\mathbb{C}) have no faithful action on R\mathbb{R}. This is identified as a special case that would establish the main conjecture under the additional assumption of noncocompactness. The source gives no resolution.

References

Primary source

Dave Witte Morris, “Some arithmetic groups that do not act on the circle”, arXiv:1210.3671 (2012).

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