# Modular cocycles and linking numbers

@article{Duke2017ModularCA,
author={William Duke and {\"O}zlem Imamoḡlu and {\'A}rp{\'a}d T{\'o}th},
journal={Duke Mathematical Journal},
year={2017},
volume={166},
pages={1179-1210}
}
• Published 15 April 2017
• Mathematics
• Duke Mathematical Journal
It is known that the 3-manifold SL(2, Z) \ SL(2, R) is diffeomorphic to the complement of the trefoil knot in S-3. E. Ghys showed that the linking number of this trefoil knot with a modular knot is given by the Rademacher symbol, which is a homogenization of the classical Dedekind symbol. The Dedekind symbol arose historically in the transformation formula of the logarithm of Dedekind's eta function under SL(2, Z). In this paper we give a generalization of the Dedekind symbol associated to a…
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