Rank-One Isometries of Buildings and Quasi-Morphisms of Kac–Moody Groups

By P. Caprace, K. Fujiwara. 2008

94 citations recorded by the source corpus.

Given an irreducible non-spherical non-affine (possibly non-proper) building X, we give sufficient conditions for a group G < Aut(X) to admit an infinite-dimensional space of non-trivial quasi-morphisms. The result applies in particular to all irreducible (non-spherical and non-affine) Kac–Moody groups over integral domains. In particular, we obtain finitely presented simple groups of infinite commutator width, thereby answering a question of Valerii G. Bardakov [MK, Prob. 14.13]. Independently of these considerations, we also include a discussion of rank-one isometries of proper CAT(0) spaces from a rigidity viewpoint. In an appendix, we show that any homogeneous quasi-morphism of a locally compact group with integer values is continuous.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b50bb54608c72891615157ad6d922f29daedc3c5

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A Characterization of Higher Rank Symmetric Spaces Via Bounded Cohomology (2007, methodology): “See [ CaF ] for another application to Kac–Moody groups.”
Characterizations of Morse Quasi-Geodesics via Superlinear Divergence and Sublinear Contraction (2016, background): “These ideas find application to Mostow rigidity in rank 1 [29], the Rank Rigidity Conjecture for CAT(0) spaces [4, 8, 11], and hyperbolicity of the curve complex of a hyperbolic surface [24, 22].”
Growth tight actions (2014, background): “The Rank Rigidity Conjecture is known to be true for many interesting classes of spaces, such as Hadamard manifolds [6], 2–dimensional, piecewise-Euclidean cell complexs [7], Davis complexes of Coxeter groups [19], universal covers of Salvetti complexes of Right Angled Artin Groups [9], and finite d”