Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 17, Number 4 (2017), 2239-2282.
The diagonal slice of Schottky space
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.
Algebr. Geom. Topol., Volume 17, Number 4 (2017), 2239-2282.
Received: 17 April 2016
Revised: 17 October 2016
Accepted: 31 October 2016
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 30F40: Kleinian groups [See also 20H10]
Secondary: 57M50: Geometric structures on low-dimensional manifolds
Series, Caroline; Tan, Ser; Yamashita, Yasushi. The diagonal slice of Schottky space. Algebr. Geom. Topol. 17 (2017), no. 4, 2239--2282. doi:10.2140/agt.2017.17.2239. https://projecteuclid.org/euclid.agt/1510841442