63 papers
The paper proves that every locally flat topological embedding of a 3-manifold into a smooth 5-manifold can be approximated by a smooth embedding via a small homotopy, thereby establishing that topologically locally flat concordance implies smooth concordance for surfaces in 4-manifolds.
GeoTop is a mathematically principled framework that unifies Topological Data Analysis and Lipschitz-Killing Curvatures to resolve the diagnostic ambiguity of topologically equivalent structures by integrating robust topological signatures with precise geometric features, thereby achieving superior accuracy and interpretability in image classification tasks such as skin lesion diagnosis.
This paper realizes homological blocks of knot complements as half-indices of 3d theories via inverted Habiro series, demonstrating that specific integration contours capture abelian flat connections while alternative pole selections yield colored Jones polynomials.