5 problems

Let $(M,\partial M)\longrightarrow (X,\partial X)$ be a degree one normal map from a topological $4$-manifold to a Poincaré pair, and suppose it is a $\mathbb{Z}[\pi_1 X]$-homology…

Let ${\rm Wh}({\rm Bor})$ denote the untwisted Whitehead double of the Borromean Rings. A link is freely topologically slice if its components bound disjoint locally flat disks in…

Cross-scale Falaco-soliton conjecture. The coherent topological features of Falaco solitons, and by extension the process of solid 2-dimensional 0-surgery, appear at both the macro…

The Borromean rings are the three-component link in the three-sphere whose components have pairwise linking number zero but are nontrivially linked together. A link is A-B slice if…

The galaxies M31 and the Milky Way are considered, together with the notion of a topological thread connecting them. Topological-thread conjecture. Based on the experimental creati…