Commentarii Mathematici Helvetici
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Published online: 2017-10-24
Simple length rigidity for Kleinian surface groups and applicationsMartin Bridgeman and Richard D. Canary (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