Characteristic structures for QFTs with defects

Let $M$ be a manifold with a tangential structure, and let $F$ be an embedded submanifold that is Poincaré dual to a characteristic class of $M$. A characteristic structure is the data of such a defect submanifold together with the corresponding characteristic information on $M$. Characteristic-structure conjecture. QFTs with defects, or impurities, inserted along particular submanifolds that are Poincaré dual to a characteristic class of $M$ are described by characteristic structures. This proposes characteristic structures as the appropriate geometric framework for studying global properties of QFT defects and impurities; the source does not provide evidence resolving the claim.