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Title: Approximate ideal structures and K-theory
We introduce a notion of approximate ideal structure for a C*-algebra, and use it as a tool to study K-theory groups. The notion is motivated by the classical Mayer-Vietoris sequence, by the theory of nuclear dimension as introduced by Winter and Zacharias, and by the theory of dynamical complexity introduced by Guentner, Yu, and the author. A major inspiration for our methods comes from recent work of Oyono-Oyono and Yu in the setting of controlled K-theory of filtered C*-algebras; we do not, however, use that language in this paper. We give two main applications. The first is a vanishing result for K-theory that is relevant to the Baum-Connes conjecture. The second is a permanence result for the Kunneth formula in C*-algebra K-theory: roughly, this says that if A can be decomposed into a pair of subalgebras (C,D) such that C, D, and C∩ D all satisfy the Kunneth formula, then A itself satisfies the Kunneth formula.  more » « less
Award ID(s):
1901522
PAR ID:
10272475
Author(s) / Creator(s):
Date Published:
Journal Name:
New York journal of mathematics
Volume:
27
ISSN:
1076-9803
Page Range / eLocation ID:
1-52
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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