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math.GT2024
Approaches to critical point theory via sequential and parametrized topological complexity
Stephan Mescher, Maximilian Stegemeyer
The Lusternik-Schnirelmann category of a space was introduced to obtain a lower bound on the number of critical points of a -function on a given manifold. Related to Lusternik…
math.GT2022
Geodesic complexity via fibered decompositions of cut loci
Stephan Mescher, Maximilian Stegemeyer
The geodesic complexity of a Riemannian manifold is a numerical isometry invariant that is determined by the structure of its cut loci. In this article we study decompositions of c…
math.GT2021
Geodesic complexity of homogeneous Riemannian manifolds
Stephan Mescher, Maximilian Stegemeyer
We study the geodesic motion planning problem for complete Riemannian manifolds and investigate their geodesic complexity, an integer-valued isometry invariant introduced by D. Rec…