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Toroidal Dehn fillings on hyperbolic 3-manifolds


About this Title

Cameron McA. Gordon and Ying-Qing Wu

Publication: Memoirs of the American Mathematical Society
Publication Year 2008: Volume 194, Number 909
ISBNs: 978-0-8218-4167-9 (print); 978-1-4704-0515-1 (online)
DOI: http://dx.doi.org/10.1090/memo/0909
MathSciNet review: 2419168
MSC: Primary 57N10; Secondary 57M50

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Table of Contents


Chapters

  • 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 $S^3$