Marked Length Rigidity for Fuchsian Buildings
نویسندگان
چکیده
We consider finite 2-complexes X that arise as quotients of Fuchsian buildings by subgroups of the combinatorial automorphism group, which we assume act freely and cocompactly. We show that locally CAT(-1) metrics on X which are piecewise hyperbolic, and satisfy a natural non-singularity condition at vertices are marked length spectrum rigid within certain classes of negatively curved, piecewise Riemannian metrics on X. As a key step in our proof, we show that the marked length spectrum function for such metrics determines the volume of X.
منابع مشابه
Mostow Rigidity for Fuchsian Buildings
We show that if a homeomorphism between the ideal boundaries of two Fuchsian buildings preserves the combinatorial cross ratio almost everywhere, then it extends to an isomorphism between the Fuchsian buildings. It follows that Mostow rigidity holds for Fuchsian buildings: if a group acts properly and cocompactly on two Fuchsian buildings X and Y , then X and Y are equivariantly isomorphic. Mat...
متن کامل1 Quasi - isometry rigidity for hyperbolic build - ings
Recall that the quasi-isometry group QI(X) of a metric space X is the set of equivalence classes of quasi-isometries f : X → X, where two quasiisometries f1, f2 are equivalent iff supx d(f1(x), f2(x)) <∞ (here we consider G as a metric space with a word metric). One approach to this question, which has been the most successful one, is to find an ‘optimal’ space X quasi-isometric to G and show t...
متن کاملTopological simplicity, commensurator super-rigidity and non-linearities of Kac-Moody groups Appendix by P. Bonvin: Strong boundaries and commensurator super-rigidity
— We provide new arguments to see topological Kac-Moody groups as generalized semisimple groups over local fields: they are products of topologically simple groups and their Iwahori subgroups are the normalizers of the pro-p Sylow subgroups. We use a dynamical characterization of parabolic subgroups to prove that some countable Kac-Moody groups with Fuchsian buildings are not linear. We show fo...
متن کاملInvestigation of the Rigidity of Floor Diaphragms on the Behavior of Concrete Tall Buildings with Staggered Shear Walls under Lateral Loading
In most cases, structural engineers assume a concrete floor to be a rigid diaphragm. Although this simplification is in most cases acceptable, it should be noted that such an assumption may be distrusted due to certain problems. Concrete structures with staggered shear walls are among those whose analysis should be conducted with special concern for the behavior of their floor diaphragms. Howev...
متن کاملOn the Set of Covolumes of Lattices for Fuchsian Buildings
We construct a nonuniform lattice and an infinite family of uniform lattices in the automorphism group of a Fuchsian building. We use complexes of groups and basic facts about spherical buildings. A consequence is that the set of covolumes of lattices for this building is nondiscrete.
متن کامل