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Transactions of the American Mathematical Society

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Bowditch's Q-conditions and Minsky's primitive stability


Authors: Jaejeong Lee and Binbin Xu
Journal: Trans. Amer. Math. Soc. 373 (2020), 1265-1305
MSC (2010): Primary 20E05, 57M60
DOI: https://doi.org/10.1090/tran/7953
Published electronically: October 28, 2019
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Abstract: For the action of the outer automorphism group of the rank two free group on the corresponding variety of $ \mathsf {PSL}(2,\mathbb{C})$ characters, two domains of discontinuity have been known to exist that are strictly larger than the set of Schottky characters. One was 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.


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Additional Information

Jaejeong Lee
Affiliation: School of Mathematics, Korea Institute for Advanced Study, 02455 Seoul, Republic of Korea
Email: jjlee@kias.re.kr

Binbin Xu
Affiliation: Mathematics Research Unit, University of Luxembourg, 6 avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxembourg
Email: binbin.xu@uni.lu

DOI: https://doi.org/10.1090/tran/7953
Received by editor(s): January 7, 2019
Received by editor(s) in revised form: July 11, 2019
Published electronically: October 28, 2019
Additional Notes: The first author is the corresponding author
The first author was supported by the grant NRF-2014R1A2A2A01005574 and NRF-2017R1A2A2A05001002.
The second author was supported by the grant DynGeo FNR INTER/ANR/15/11211745.
Article copyright: © Copyright 2019 American Mathematical Society