Relative rigidity, quasiconvexity and \(C\)-complexes. (Q1007163)

The author introduces and studies the notion of relative rigidity. In an essential part this is based on the previous work of Bowditch, Farb, Kapovich, Kleiner, Leeb, Mosher, Mostow, Sageev, Schwartz and others on quasi-isometries, rigidity and hyperbolic groups. The results concern proving relative rigidity in certain important cases. The main arguments are inspired by the work of \textit{G. D. Mostow} [Strong rigidity of locally symmetric spaces. Ann. Math. Stud. 78, Princeton: Princeton University Press and University of Tokyo Press (1973; Zbl 0265.53039)] and \textit{R. E. Schwartz} [Invent. Math. 128, No. 1, 177-199 (1997; Zbl 0884.58021)]. The reader should be warned that there are errors in the printed list of references, in particular, the reference to the above mentioned paper by Schwartz is missing.