3 problems

Kervaire's classification conjecture. The $5$-th Betti number $B_5(M)$ and Kervaire invariant $\Phi(M)\in \mathbb{Z}_2$ are a complete set of invariants of the homotopy type of $M$…

Let $M$ be a PL $n$-manifold, let $\Delta(M)$ denote its complexity, and define its sum-stable complexity by … The limit exists by subadditivity. Sum-stable complexity conjecture.…

Let $M$ be a closed connected prime orientable PL $4$-manifold, and let $\mathcal{G}(M)$ denote its regular genus. Spaggiari's conjecture. If $\mathcal{G}(M)=6$, then $M$ is topolo…