2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61199We give a survey of cyclic homology/cohomology theory including a detailed discussion of cyclic theories for various classes of topological algebras. We show how to associate cyclic classes with Fredholm modules and $K$-theory classes and how to construct a completely general bivariant Chern-Connes character from bivariant $K$-theory to bivariant cyclic theory.Operator AlgebrasK-Theory and Homology14F40, 19K99, 19E20, 46L87, 56A12, 58G12text