I will survey recent work (joint with N. Bergeron and P. Charollois) giving a new construction of certain cohomology classes of $SL_N(\mathbb{Z})$ that were first defined by Nori and Szcech. To motivate our approach, I will start by discussing the problem of how to compute linking numbers in certain three-manifolds that fiber over the circle, e.g in the complement of the trefoil knot in the 3-sphere. We will see that these linking numbers are special values of L-functions, which implies that the latter are rational numbers. Then I will explain some generalizations that relate the topology of real locally symmetric spaces with the arithmetic world of modular forms.