4 papers
Canonical chain complexes for Morse-Smale vector fields
Clemens Bannwart, Claudia Landi
In 1960, Smale defined a filtration of a closed smooth manifold by the unstable manifolds of fixed points and closed orbits of a Morse-Smale vector field defined on it, and derived…
Sufficient Conditions for the Shrinking Wellness Lemma
Clemens Bannwart
The well groups were introduced by Edelsbrunner, Morozov, and Patel to measure the robustness of geometric features of a function with respect to perturbations. Roughly speaking, t…
Tagged barcodes for the topological analysis of gradient-like vector fields
Clemens Bannwart, Claudia Landi
Intending to introduce a method for the topological analysis of fields, we present a pipeline that takes as an input a weighted and based chain complex, produces a factored chain c…
About non-uniqueness when removing closed orbits in Morse-Smale vector fields
Clemens Bannwart
Given a Morse-Smale vector field on a smooth manifold, Franks described how one can replace a closed orbit of index by two rest points of index and , using a local per…