The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Commentarii Mathematici Helvetici


Full-Text PDF (568 KB) | Metadata | Table of Contents | CMH summary
Online access to the full text of Commentarii Mathematici Helvetici is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
subscriptions@ems-ph.org
Volume 92, Issue 4, 2017, pp. 715–750
DOI: 10.4171/CMH/422

Published online: 2017-10-24

Simple length rigidity for Kleinian surface groups and applications

Martin Bridgeman[1] and Richard D. Canary[2]

(1) Boston College, Chestnut Hill, USA
(2) University of Michigan, Ann Arbor, USA

We prove that a Kleinian surface group is determined, up to conjugacy in the isometry group of $\mathbb H^3$, by its simple marked length spectrum. As a first application, we show that a discrete faithful representation of the fundamental group of a compact, acylindrical, hyperbolizable 3-manifold $M$ is similarly determined by the translation lengths of images of elements of $\pi_1(M)$ represented by simple curves on the boundary of $M$. As a second application, we show the group of diffeomorphisms of quasifuchsian space which preserve the renormalized pressure intersection is generated by the (extended) mapping class group and complex conjugation.

Keywords: Kleinian surface groups, length spectrum and rigidity

Bridgeman Martin, Canary Richard: Simple length rigidity for Kleinian surface groups and applications. Comment. Math. Helv. 92 (2017), 715-750. doi: 10.4171/CMH/422