By N. Christopher Phillips
Freeness of an motion of a compact Lie crew on a compact Hausdorff area is such as an easy at the corresponding equivariant K-theory. This truth might be considered as a theorem on activities on a commutative C*-algebra, specifically the algebra of constant complex-valued features at the area. The successes of "noncommutative topology" recommend that one may still try and generalize this end result to activities on arbitrary C*-algebras. missing a suitable definition of a loose motion on a C*-algebra, one is led in its place to the research of activities pleasurable stipulations on equivariant K-theory - within the situations of areas, easily freeness. the 1st 3rd of this booklet is a close exposition of equivariant K-theory and KK-theory, assuming just a normal wisdom of C*-algebras and a few traditional K-theory. It maintains with the author's study on K-theoretic freeness of activities. it really is proven that many houses of freeness generalize, whereas others don't, and that definite types of K-theoretic freeness are regarding different noncommutative measures of freeness, comparable to the Connes spectrum. the results of K-theoretic freeness for activities on style I and AF algebras also are tested, and in those situations K-theoretic freeness is characterised analytically.
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