Kleinian group

Definition

The term Kleinian group is used for any closed subgroup of projective special linear group:PSL(2,C) (the projective special linear group of degree two $PSL(2,\mathbb {C} )$ over the field of complex numbers) that is discrete in the subspace topology. Note that we are using the natural topology on $PSL(2,\mathbb {C} )$ arising as a quotient topology from $SL(2,\mathbb {C} )$, which in turn acquires a subspace topology from the space of $2\times 2$ matrices over $\mathbb {C}$, which in turn is identified with $\mathbb {C} ^{4}\cong \mathbb {R} ^{8}$.