Árpád Tóth

Modular cocycles and linking numbers

I will review Ghys' work on the geodesic flow on the 3-manifold SL(2;Z)\SL(2;R). This 3-manifold is homeomorphic to the complement of the trefoil knot in S^3. Closed geodesics on the classical modular curve give rise to knots whose linking number with the trefoil is connected to the transformation formula of the logarithm of Dedekind's eta-function. In the end I will outline how to associate a similar function to a fixed closed geodesic.