Discrete primitive-stable representations with large rank surplus

Minsky, Yair N; Moriah, Yoav

doi:10.2140/gt.2013.17.2223

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Discrete primitive-stable representations with large rank surplus

Yair N Minsky and Yoav Moriah

Geometry & Topology 17 (2013) 2223–2261

DOI: 10.2140/gt.2013.17.2223

Abstract

We construct a sequence of primitive-stable representations of free groups into ${PSL}_{2} (ℂ)$ 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.

Keywords

primitive stable, Whitehead graph, representation, rank, Dehn filling

Mathematical Subject Classification 2010

Primary: 57M60

Secondary: 57M50, 57M05

References

Publication

Received: 30 September 2010

Revised: 16 October 2012

Accepted: 25 April 2013

Published: 30 July 2013

Proposed: Martin Bridson

Seconded: Danny Calegari, Benson Farb

Authors

Yair N Minsky
Department of Mathematics Yale University PO Box 208283 New Haven, CT 06520 USA
http://www.math.yale.edu/users/yair
Yoav Moriah
Department of Mathematics Technion 32000 Haifa Israel
http://www.math.technion.ac.il/~ymoriah/

Volume 17, issue 4 (2013)