2-dimensional stratifolds
J.C.G\'omez-Larra\~naga, F.Gonz\'alez-Acu\~na, Wolfgang Heil
TL;DR
This paper introduces 2-stratifolds, a generalization of 2-manifolds with applications in topology and data analysis, and investigates their properties through associated labeled graphs.
Contribution
It defines 2-stratifolds and analyzes properties of their labeled graphs to determine simple connectivity, advancing understanding of their topological structure.
Findings
Labeled graphs determine simple connectivity of 2-stratifolds.
Characterization of simply connected 2-stratifolds.
Potential applications in topological data analysis.
Abstract
2-stratifolds are a generalization of 2-manifolds in that there are disjoint simple closed curves where several sheets meet. They arise in the study of categorical invariants of 3-manifolds and may have applications to topological data analysis. We define 2-stratifolds and study properties of their associated labeled graphs that determine which ones are simply connected.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Advanced Neuroimaging Techniques and Applications