4 problems

Let $n\geq 3$ be odd, let $W_{g,1}$ denote the corresponding high-dimensional manifold, and consider the stabilization maps on rational homology … An optimal stability bound should…

Wang–Xu conjecture. The dimensions without exotic spheres are exactly $1,2,3$, possibly $4$, and $5,6,12,56,61$.

Poincaré-conjecture consequence. The monoid ${\mathcal M^{\mathrm{Top}}_{n}}$ never has non-trivial units, and ${\mathcal M^{\mathrm{PL}}_{n}}$ has no non-trivial units except pote…

Let $W_g=\#^g S^n\times S^n$, let $B\operatorname{Tor}(W_g,D^2)$ be the classifying space of the Torelli group relative to a disc, and let…