In this paper, we extend the concepts of movability, strong movability, AWR and AWNR for arbitrary metrizable spaces and we show that MAR and AWR are the same concept and that MANR, strong movability and movable AWNR are the same concept. And we prove that the projection of the product X × Y of a locally compact metric space X and an MAR Y onto X induces the shape equivalence and that the inclusion of a metric space X into a union X \cup Y of X and an MAR Y induces a shape equivalence if X and Y are closed in X \cup Y and if X \cap Y is an MAR.
The purpose of this paper is the construction and cohomological study of semi-simplicial models for the Weil algebra of a Lie algebra. The geometric context where the authors introduced these algebras is the construction of generalized characteristic classes for foliated bundles. There are two main aspects to the results of this paper. The first is the homological equivalence of all semi-simplicial Weil algebras even after passing to basic elements with respect to a subalgebra and to quotients by certain characteristic filtration ideals. The geometric consequence is that the generalized characteristic homomorphisms defined on these various complexes all have the same domain of universal generalized characteristic invariants. The second aspect is a comparison map from the ordinary Weil algebra to the semi-simplicial Weil algebra realizing a homology isomorphism after passing to basic elements with respect to a subalgebra and to quotients by characteristic filtration ideals. The geometric consequence is a comparison of the characteristic class constructions on the various complexes considered, which is also of significance for explicit computations.
We give a generalization of the theorems of the existence (see [9]) and the uniqueness (see [3]) of the contractive intertwining dilations in the presence of some representations of a C*-algebra.