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Article History

Received: 18 June 2015

Accepted: 13 August 2015

First Online: 15 May 2016

Acknowledgements

: I would like to thank Matt Bainbridge, Steven Gortler, Richard Kenyon, Sarah Koch, Tan Lei, Dan Margalit, and Giulio Tiozzo for many helpful conversations. I would also like to thank especially Maxime Fortier Bourque, who pointed me towards Ioffe’s theorem [] and had numerous other insights. This project grew out of extensive conversations with Kevin Pilgrim, who helped shape my understanding of the subject in many ways. Many of the arguments were developed jointly with him. Notably, he communicated Theorem 8.4 to me, and Theorem 4 is joint work with him. Theorem 5 is joint work with Jeremy Kahn, who also contributed substantially throughout. Above all, I would like to thank William Thurston for introducing me to the subject and insisting on understanding deeply. This work was partially supported by NSF grants DMS-1358638 and DMS-1507244.

: The author declares that he has no competing interests.