Abstract: Arithmetic subgroups of PSL(2,C) provide a large class of hyperbolic 3-manifolds exhibiting a lot of interactions between geometry, topology and number theory. In this talk, I will give examples of arithmetic hyperbolic manifolds in dimension 2 and 3 with the goal to illustrate the connections between geometrical, topological and number theoretical aspects of these manifolds. I will discuss various invariants and techniques that are useful in distinguishing arithmetic and non-arithmetic manifolds. Finally, I will discuss some observations related to the question of arithmeticity of modular knots.
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