Stability in the Cuntz semigroup of a commutative C*-algebra

Abstract

We prove stability theorems in the Cuntz semigroup of a commutative C*-algebra which are analogues of classical stability theorems for topological vector bundles over compact Hausdorff spaces. Several applications to simple unital AH algebras of slow dimension growth are then given: such algebras have strict comparison of positive elements; their Cuntz semigroups are recovered functorially from the Elliott invariant; the lower-semicontinuous dimension functions are dense in the space of all dimension functions, and the latter is a Choquet simplex.

26 pages, minor revisions, to appear in Proc. LMS

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Cited by in corpus (8)

• Comparison theory and smooth minimal C*-dynamics
• The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras
• On Local AH algebras
• The minimal ideal in multiplier algebras
• The cone of lower semicontinuous traces on a C*-algebra
• High-dimensional Z-stable AH algebras
• Rank Constrained Homotopies
• An algebraic approach to the radius of comparison