### Modular cocycles and linking numbers

Heilbronn Number Theory Seminar

30th January 2019, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

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.

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