The Index of Manifolds with Toral Actions and Geometric Interpretations of the ... (..., (S1, Mn)) Invariant of Atiyah and Singer.
We show that the geometric realization of a cyclic set has a natural, -equivariant, cellular decomposition. As an application, we give another proof of a well-known isomorphism between cyclic homology of a cyclic space and -equivariant Borel homology of its geometric realization.