Stabilization of Exotic Surfaces in 4-Manifolds: Internal and External Approaches
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.
Calculating the Kauffman Bracket Skein Module of Small Seifert Manifolds
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.
Efficient Computation of Singular Homology and Homotopy Groups of Finite Directed Graphs via Directed Vietoris-Rips Complexes
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.
Computing the Matching Distance Between 2-Parameter Persistence Modules Using Critical Values
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.
Formalizing the Proof that the Fourth Homotopy Group of the 3-Sphere is Z/2Z in Cubical Agda
The fourth homotopy group of the 3-sphere, π4(S3), is isomorphic to Z/2Z.
Rapid and Precise Topological Comparison of Merge Trees using Neural Networks
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.
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