Homotopy invariance of entire current cyclic homology (Q1388207)

Homology theory of De Rham currents is dual to the cohomology of differential forms with compact support. The De Rham current homology is well developed and has applications in many problems in mathematical physics, geometry, etc. Cohomology theory of differential forms on manifolds is well investigated by \textit{A. Connes} et al. as a cyclic cohomology. In a paper of \textit{M. Khalkhali} the so-called entire cyclic cohomology \(HE^*\) is considered as an infinite cyclic cohomology and two main properties of this theory are proved: the homotopy invariance and the Morita invariance. In the present paper the authors use the results of Khalkhali restricting a non-commutative analogue of differential forms with compact support to ideals with ad-invariant trace, and they construct the dual to the entire cyclic cohomology of a projective limit of ideals with ad-invariant trace and prove its homotopy invariance.