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See detailBowditch's Q-conditions and Minsky's primitive stability
Lee, Jaejeong; Xu, Binbin UL

E-print/Working paper (2018)

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 ... [more ▼]

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. [less ▲]

Detailed reference viewed: 110 (12 UL)
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See detailCARRIER GRAPHS FOR REPRESENTATIONS OF THE RANK TWO FREE GROUP INTO ISOMETRIES OF HYPERBOLIC THREE SPACE
Tan, Ser Peow; Xu, Binbin UL

E-print/Working paper (2018)

Carrier graphs were first introduced for closed hyperbolic 3-manifolds by White. In this paper, we first generalize this definition to carrier graphs for representations of a rank two free group into the ... [more ▼]

Carrier graphs were first introduced for closed hyperbolic 3-manifolds by White. In this paper, we first generalize this definition to carrier graphs for representations of a rank two free group into the isometry group of hyperbolic three space. Then we prove the existence and the finiteness of minimal carrier graphs for those representations which are discrete, faithful and geometrically finite, and more generally, those that satisfy certain finiteness conditions first introduced by Bowditch. [less ▲]

Detailed reference viewed: 66 (2 UL)