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2017 The diagonal slice of Schottky space
Caroline Series, Ser Tan, Yasushi Yamashita
Algebr. Geom. Topol. 17(4): 2239-2282 (2017). DOI: 10.2140/agt.2017.17.2239

Abstract

An irreducible representation of the free group on two generators X,Y into SL(2, ) is determined up to conjugation by the traces of X,Y and XY . If the representation is faithful and discrete, the resulting manifold is in general a genus-2 handlebody. We study the diagonal slice of the representation variety in which TrX = TrY = TrXY . 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 X,Y have traces in [2,2], and at most finitely many primitive elements have traces with absolute value at most 2. The graphics make clear that this set is both strictly larger than, and significantly different from, the discreteness locus.

Citation

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Caroline Series. Ser Tan. Yasushi Yamashita. "The diagonal slice of Schottky space." Algebr. Geom. Topol. 17 (4) 2239 - 2282, 2017. https://doi.org/10.2140/agt.2017.17.2239

Information

Received: 17 April 2016; Revised: 17 October 2016; Accepted: 31 October 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06762690
MathSciNet: MR3685607
Digital Object Identifier: 10.2140/agt.2017.17.2239

Subjects:
Primary: 30F40
Secondary: 57M50

Rights: Copyright © 2017 Mathematical Sciences Publishers

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