"Volume 194, number 909 (end of volume)."

"July 2008."

Includes bibliographical references (p. 139-140).

1. Introduction 2. Preliminary lemmas 3. $\hat \Gamma ^+_a$ has no interior vertex 4. Possible components of $\hat \Gamma ^+_a$ 5. The case $n_1$, $n_2 > 4$ 6. Kleinian graphs 7. If $n_a = 4$, $n_b \geq 4$ and $\hat \Gamma ^+_a$ has a small component then $\Gamma _a$ is kleinian 8. If $n_a = 4$, $n_b \geq 4$ and $\Gamma _b$ is non-positive then $\hat \Gamma ^+_a$ has no small component 9. If $\Gamma _b$ is non-positive and $n_a = 4$ then $n_b \leq 4$ 10. The case $n_1 = n_2 = 4$ and $\Gamma _1$, $\Gamma _2$ non-positive 11. The case $n_a = 4$, and $\Gamma _b$ positive 12. The case $n_a = 2$, $n_b \geq 3$, and $\Gamma _b$ positive 13. The case $n_a = 2$, $n_b > 4$, $\Gamma _1$, $\Gamma _2$ non-positive, and $\max (w_1 + w_2, w_3 + w_4) = 2n_b - 2$ 14. The case $n_a = 2$, $n_b > 4$, $\Gamma _1$, $\Gamma _2$ non-positive, and $w_1 = w_2 = n_b$ 15. $\Gamma _a$ with $n_a \leq 2$ 16. The case $n_a = 2$, $n_b = 3$ or $4$, and $\Gamma _1$, $\Gamma _2$ non-positive 17. Equidistance classes 18. The case $n_b = 1$ and $n_a = 2$ 19. The case $n_1 = n_2 = 2$ and $\Gamma _b$ positive 20. The case $n_1 = n_2 = 2$ and and both $\Gamma _1$, $\Gamma _2$ non-positive 21. The main theorems 22. The construction of $M_i$ as a double branched cover 23. The manifolds $M_i$ are hyperbolic 24. Toroidal surgery on knots in $S^3$

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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