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The diagonal slice of
Schottky space
Caroline Series, Ser Peow Tan and Yasushi Yamashita |
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Algebraic & Geometric Topology 17 (2017) 2239–2282
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Abstract |
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An irreducible representation of the free group on two generators into is determined up to conjugation by the traces of and . If the representation is faithful and discrete, the resulting manifold is in general a genus- handlebody. We study the diagonal slice of the representation variety in which . Using the symmetry, we are able to compute the Keen–Series pleating rays and thus fully determine the locus of faithful discrete representations. We also computationally determine the “Bowditch set” consisting of those parameter values for which no primitive elements in have traces in , and at most finitely many primitive elements have traces with absolute value at most . The graphics make clear that this set is both strictly larger than, and significantly different from, the discreteness locus. |
Keywords
Schottky group, nondiscrete group, primitive element,
Bowditch condition
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Mathematical Subject Classification 2010
Primary: 30F40
Secondary: 57M50
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References |
Publication
Received: 17 April 2016
Revised: 17 October 2016
Accepted: 31 October 2016
Published: 3 August 2017
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Authors |
| Caroline Series | |
| Mathematics Institute University of Warwick Leeman Building Coventry CV4 7AL United Kingdom |
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| http://homepages.warwick.ac.uk/~masbb/ | |
| Ser Peow Tan | |
| Department of Mathematics National University of Singapore Block S17, 10 Lower Kent Ridge Rd. Singapore 119076 |
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| http://www.math.nus.edu.sg/~mattansp/ | |
| Yasushi Yamashita | |
| Department of Information and
Computer Sciences Nara Women’s University Kitauoyanishi-machi, Nara 630-8506 Japan |
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| http://vivaldi.ics.nara-wu.ac.jp/~yamasita/ | |
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