30 nov 2016 -- 14:30
Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
It is known that the 3-manifold SL(2,Z)\SL(2,R) is diffeomorphic to the complement of the trefoil knot in S3 . E. Ghys showed that the linking number of the trefoil knot with a modular knot is given in terms 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 talk I will give a generalization of the Dedekind symbol associated to a fixed modular knot and show its relation to the linking numbers of two modular knots. This is joint work with W. Duke and A. Toth.