# Fiber products of rank 1 superrigid lattices and quasi-isometric embeddings

@inproceedings{Tsouvalas2021FiberPO, title={Fiber products of rank 1 superrigid lattices and quasi-isometric embeddings}, author={Konstantinos Tsouvalas}, year={2021} }

Let Γ be an irreducible lattice of a real algebraic semisimple Lie group G. If Γ is cocompact, then the inclusion of Γ in G is a quasi-isometric embedding. More precisely, if we equip the symmetric space G/K associated to G with the left invariant Riemannian distance dG/K induced by the Killing metric, and identify (via the orbit map) Γ as a subset of G/K, then dG/K restricted on Γ is coarsely equivalent with any left invariant word metric on Γ induced by a finite generating subset. If Γ is not…

## One Citation

### Cartan projections of fiber products and non quasi-isometric embeddings

- Mathematics
- 2022

. Let Γ be a ﬁnitely generated group and N be a normal subgroup of Γ. The ﬁber product of Γ with respect to N is the subgroup Γ × N Γ = (cid:8) ( γ,γw ) : γ ∈ Γ ,w ∈ N (cid:9) of the direct product Γ…

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