Geometry & Topology

Discrete primitive-stable representations with large rank surplus

Yair N Minsky and Yoav Moriah

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Abstract

We construct a sequence of primitive-stable representations of free groups into PSL2() whose ranks go to infinity, but whose images are discrete with quotient manifolds that converge geometrically to a knot complement. In particular this implies that the rank and geometry of the image of a primitive-stable representation imposes no constraint on the rank of the domain.

Article information

Source
Geom. Topol., Volume 17, Number 4 (2013), 2223-2261.

Dates
Received: 30 September 2010
Revised: 16 October 2012
Accepted: 25 April 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732651

Digital Object Identifier
doi:10.2140/gt.2013.17.2223

Mathematical Reviews number (MathSciNet)
MR3109867

Zentralblatt MATH identifier
1278.57026

Subjects
Primary: 57M60: Group actions in low dimensions
Secondary: 57M50: Geometric structures on low-dimensional manifolds 57M05: Fundamental group, presentations, free differential calculus

Keywords
primitive stable Whitehead graph representation rank Dehn filling

Citation

Minsky, Yair N; Moriah, Yoav. Discrete primitive-stable representations with large rank surplus. Geom. Topol. 17 (2013), no. 4, 2223--2261. doi:10.2140/gt.2013.17.2223. https://projecteuclid.org/euclid.gt/1513732651


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