Many explicit examples of exotic pairs of surfaces in a smooth 4-manifold become smoothly isotopic after one external stabilization with S2 × S2 or CP2#CP2. The stabilizing manifold depends on the construction and parametrization of the surfaces.
This paper provides a presentation of the Kauffman bracket skein module for each small Seifert manifold S2(k1, k2, k3), where ki are integers. The authors demonstrate how to obtain the Kauffman bracket skein module of lens spaces from their main theorem.
The directed Vietoris-Rips complex of a finite directed graph is weakly homotopy equivalent to the original graph, allowing for efficient computation of its singular homology and homotopy groups.
The matching distance between two 2-parameter persistence modules can be computed exactly by considering a finite set of lines passing through critical values and switch points in the parameter space.
The fourth homotopy group of the 3-sphere, π4(S3), is isomorphic to Z/2Z.
A novel Merge Tree Neural Network (MTNN) model that leverages graph neural networks and a topological attention mechanism to enable rapid and precise comparison of merge trees.