McNamara–Vafa cobordism conjecture

Let $c9$ be a tangential structure, and suppose a consistent $n$-dimensional theory of quantum gravity sums over spacetime backgrounds carrying a $c9$-structure. The associated bordism groups are denoted by $a9_k^\xi$. McNamara–Vafa cobordism conjecture. For $3\le k\le n-1$,

$$\Omega_k^\xi=0.$$

The conjecture expresses the expectation that consistent quantum-gravitational theories have no global symmetries detected by these bordism groups. Its applicability to the heterotic and CHL tangential structures is one of the paper's main physical motivations; the source does not state a resolution.