The density conjecture for Kleinian groups

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Let GG be a finitely generated group. Let AH⁡(G)\operatorname{AH}(G) denote the space of algebraic limits of discrete faithful representations and let MP⁡(G)\operatorname{MP}(G) denote the minimally parabolic geometrically finite representations, as in the source. Density conjecture.

AH⁡(G) is the closure of MP⁡(G).\operatorname{AH}(G) \text{ is the closure of } \operatorname{MP}(G).

The conjecture asks whether every algebraic limit is approximable by geometrically finite minimally parabolic representations. The source presents this as a natural question and gives no resolution status.

References

Primary source

James W. Anderson, “A brief survey of the deformation theory of Kleinian groups”, arXiv:math/9810186 (1998).

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