The visual core of a hyperbolic 3-manifold

Algebraic invariants, mutation, and commensurability of link complements

“…, and the result follows from the equation at the bottom of [23, p. 76]. See [5], Proposition 5.2 and the remarks after 5.3 for related results.…”

“…The fact above implies that Γ 0 and Γ 1 which meet cute along a hyperplane K satisfy the hypotheses of [23,Theorem 8.2], from which the grouptheoretic conclusions above thus follow. That the desired isometry exists follows from the remarks in [23] below Theorem 8.2, which have since been considerably fleshed out in Anderson-Canary's "The visual core of a hyperbolic manifold" [5].…”

“…Remark. If k is algebraically closed, the relation (4) above, called the five term relation, implies (5). For instance, taking √ z and √ z −1 as x and y, respectively, in (4), then interchanging their roles and summing the results yields [z] + [1/z] = 0.…”