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Conference on Noncommutative Geometry and Global Analysis in Honor of Henri Moscovici, Bonn, Germany, 29 June - 04 July 2009, vol.546, pp.171-179
In 1998 Alain Connes and Henri Moscovici invented a cohomology theory for Hopf algebras and a characteristic map associated with the cohomology theory in order to solve a specific technical problem in transverse index theory. In the following decade, the cohomology theory they invented developed on its own under the name Hopf-cyclic cohomology. But the history of Hopf-cyclic cohomology and the characteristic map they invented remained intricately linked. In this survey article, we give an account of the development of the characteristic map and Hopf-cyclic cohomology.