2 problems

Pin-plus conjecture. The conclusion of the preceding Wu-class vanishing theorem does not hold for $\operatorname{Pin}^+$ manifolds in dimension $8k+2$, but every such manifold neve…

Let $(B_*,\beta)$ be a chain bundle with algebraic Wu class $\widehat v_{2k}(\beta)$, and let $\operatorname{ev}$ denote evaluation on homology. Let $\Sigma$, $\Sigma_8$, $\Lambda$…