A TOPOLOGICAL INVARIANT FOR CONTINUOUS FIELDS OF CUNTZ ALGEBRAS II

We investigate an invariant for continuous fields of the Cuntz al-gebra On+1 introduced by Taro Sogabe [Math. Ann. 380 (2021), pp. 91-117], and find a way to obtain a continuous field of Mn(O-infinity) from that of On+1 using the construction of the invariant. By Brown's representability theorem, this gives a bijection from the set of the isomorphism classes of continuous fields of On+1 to those of Mn(O-infinity). As a consequence, we obtain a new proof for M. Dadarlat's classification result of continuous fields of On+1 arising from vector bundles, which corresponds to those of Mn(O-infinity) stably isomorphic to the trivial field.