# Modular cocycles and linking numbers

@article{Duke2017ModularCA, title={Modular cocycles and linking numbers}, 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} }

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…

## 11 Citations

Modular knots, automorphic forms, and the Rademacher symbols for triangle groups

- Mathematics
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´E. Ghys proved that the linking numbers of modular knots and the “missing” trefoil K 2 , 3 in S 3 coincide with the values of a highly ubiquitous function called the Rademacher symbol for SL 2 Z .…

A Hyperbolic Analogue of the Rademacher Symbol.

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One of the most famous results of Dedekind is the transformation law of $\log \Delta(z)$. After a half-century, Rademacher modified Dedekind's result, and introduced an…

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For any noncocompact Fuchsian group $\Gamma$, we show that periods of the canonical differential of the third kind associated to residue divisors of cusps are expressed in terms of Rademacher symbols…

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We refine McMullen’s construction of sequences of knots in S obeying the Chebotarev law in two ways. One is to extend his theorem for generalized pseudo-Anosov flows, which may admit a finite number…

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We prove a geometric formula for the cycle integrals of Parson’s weight 2k modular integrals in terms of the intersection angles of geodesics on modular curves. Our result is an analog for modular…

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We study the weight 2 parabolic/elliptic/hyperbolic Eisenstein series, which gives a harmonic/polar harmonic/locally harmonic Maass form, simultaneously. Furthermore, by means of the hyperbolic…

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We give some new applications of Kronecker’s first limit formula to real quadratic fields. In particular, we give a surprising geometrical relationship between the CM points associated with two…

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