A topological invariant for continuous fields of the Cuntz algebras

2020/02/17 by Sogabe, Taro
#46L80 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2002.06807

Abstract

For a continuous field of the Cuntz algebra over a finite CW complex, we introduce a topological invariant, which is an element in Dadarlat-Pennig's generalized cohomology group, and prove that the invariant is trivial if and only if the field comes from a vector bundle via Pimsner's construction.

Related

• A topological invariant for continuous fields of Cuntz algebras II
• The Cuntz semigroup of continuous fields
• The C*-algebra of a vector bundle
• Geometric Structure of Dimension Functions of Certain Continuous Fields
• The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra