QUASI-ISOMETRIC EMBEDDINGS INAPPROXIMABLE BY ANOSOV REPRESENTATIONS

We construct examples of quasi-isometric embeddings of word hyperbolic groups into SL(d,R) for d >= 4 which are not limits of Anosov representations into SL(d,R). As a consequence, we conclude that an analogue of the density theorem for PSL(2,C) does not hold for SL(d, R) when d >= 4.

Automated summary

This article presents examples of quasi-isometric embeddings of word hyperbolic groups into SL(d,R) for d >= 4, which are not limits of Anosov representations into SL(d,R). Consequently, it is concluded that an analogue of the density theorem for PSL(2,C) does not hold for SL(d, R) when d >= 4.