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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Bowditch’s Q-conditions and Minsky’s primitive stability
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by Jaejeong Lee and Binbin Xu PDF
Trans. Amer. Math. Soc. 373 (2020), 1265-1305 Request permission

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
  • MR Author ID: 1160974
  • 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
  • MR Author ID: 1184417
  • Email: binbin.xu@uni.lu
  • 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.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 1265-1305
  • MSC (2010): Primary 20E05, 57M60
  • DOI: https://doi.org/10.1090/tran/7953
  • MathSciNet review: 4068264