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math.AT2025
A Unified View on the Functorial Nerve Theorem and its Variations
Ulrich Bauer, Michael Kerber, Fabian Roll +1
The nerve theorem is a basic result of algebraic topology that plays a central role in computational and applied aspects of the subject. In topological data analysis, one often nee…
math.AT2024
Wrapping Cycles in Delaunay Complexes: Bridging Persistent Homology and Discrete Morse Theory
Ulrich Bauer, Fabian Roll
We study the connection between discrete Morse theory and persistent homology in the context of shape reconstruction methods. Specifically, we consider the construction of Wrap com…