Invisible Lawson brackets with nontorsion singular classes

Construct an integral nonzero Lawson bracket invisible to singular homology for which all three associated singular homology classes have infinite order.

Background

The paper constructs integral Lawson–Massey brackets whose quotient classes are nonzero and whose selected values map to zero under the Lawson cycle map. A perturbation produces examples in which all three associated singular homology classes are nonzero, but the first and third classes still have order two, while the middle class has infinite order.

The paper explicitly leaves unresolved whether the same invisibility phenomenon can occur when every one of the three singular homology classes is nontorsion. The transfer constructions used in the paper preserve the torsion nature of the relevant classes and therefore do not settle this question.