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Tracially Complete C*-Algebras
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We introduce a new class of operator algebras -- tracially complete C*-algebras -- as a vehicle for transferring ideas and results between C*-algebras and their tracial von Neumann algebra completions. We obtain structure and classification results for amenable tracially complete C*-algebras satisfying an appropriate version of Murray and von Neumann's property gamma for II_1 factors. In a precise sense, these results fit between Connes' celebrated theorems for injective II_1 factors and the unital classification theorem for separable simple nuclear C*-algebras. The theory also underpins arguments for the known parts of the Toms-Winter conjecture.
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Cited by 1 Pith paper
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Schubert Calculus and uniform property $\Gamma$
Constructs a nuclear C*-algebra without uniform property Γ via a new obstruction from Thom-Porteous degeneracy loci and quadratic Schubert calculus that forces dimension growth.
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