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A discrete group $\Gamma \leq \operatorname{PSL}(2, \mathbb{C})$ is said to be Fuchsian if its limit set is a geometric circle on $\partial \mathbb{H}^3$. If its limit set is a Jordan curve and no element of $\Gamma$ interchanges the complementary components of the limit set, then $\Gamma$ is said to be quasifuchsian.

    A discrete group $\Gamma \leq \operatorname{PSL}(2, \mathbb{C})$ is said to be Fuchsian if its limit set is a geometric circle on $\partial \mathbb{H}^3$. If its limit set is a Jordan curve and no element of $\Gamma$ interchanges the complementary components of the limit set, then $\Gamma$ is said to be quasifuchsian.

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Hyperbolic Knot Theory

Hyperbolic Knot Theory

Jessica S. Purcell 1st Edition

Chapter 12, Problem 10

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A discrete group $\Gamma \leq \operatorname{PSL}(2, \mathbb{C})$ is a group of transformations acting on the hyperbolic space $\mathbb{H}^3$. The limit set of $\Gamma$ is the set of accumulation points of the orbit of a point in $\mathbb{H}^3$ under the action of Show more…

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A discrete group $\Gamma \leq \operatorname{PSL}(2, \mathbb{C})$ is said to be Fuchsian if its limit set is a geometric circle on $\partial \mathbb{H}^3$. If its limit set is a Jordan curve and no element of $\Gamma$ interchanges the complementary components of the limit set, then $\Gamma$ is said to be quasifuchsian.

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