Bowditch's Q-conditions and Minsky's primitive stability
arXiv:1812.04237 · doi:10.1090/tran/7953
Abstract
For the action of the outer automorphism group of the rank two free group on the corresponding variety of PSL(2,C) characters, two domains of discontinuity have been known to exist that are strictly larger than the set of Schottky characters. One is introduced by Bowditch in 1998 (followed by Tan, Wong and Zhang in 2008) and the other by Minsky in 2013. We prove that these two domains are equal. We then show that they are contained in the set of characters having what we call the bounded intersection property.
arXiv comment47 pages, 17 figures; [v2] incorporated referee's suggestions; [v3] added the injectivity condition in the second statement of Theorem II that was assumed implicitly in the proof. The statement remains open without the condition. We thank Caroline Series for pointing this out to us
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