Simple length rigidity for Kleinian surface groups and applications

  • Martin Bridgeman

    Boston College, Chestnut Hill, USA
  • Richard D. Canary

    University of Michigan, Ann Arbor, USA


We prove that a Kleinian surface group is determined, up to conjugacy in the isometry group of , 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 is similarly determined by the translation lengths of images of elements of represented by simple curves on the boundary of . 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.

Cite this article

Martin Bridgeman, Richard D. Canary, Simple length rigidity for Kleinian surface groups and applications. Comment. Math. Helv. 92 (2017), no. 4, pp. 715–750

DOI 10.4171/CMH/422