Simple length rigidity for Kleinian surface groups and applications
Abstract
We prove that a Kleinian surface groups 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 intersection number is generated by the (extended) mapping class group and complex conjugation.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2015
- DOI:
- arXiv:
- arXiv:1509.02510
- Bibcode:
- 2015arXiv150902510B
- Keywords:
-
- Mathematics - Geometric Topology;
- Mathematics - Differential Geometry
- E-Print:
- doi:10.1112/plms/pdv064