6 citations · 21 across the 10 of their papers we have counts for
7 papers · 1 filter
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…
Geometric and topological properties of manifolds in robot motion planning
Stephan Mescher
Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of…
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…
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…
Spherical complexities, with applications to closed geodesics
Stephan Mescher
We construct and discuss new numerical homotopy invariants of topological spaces that are suitable for the study of functions on loop and sphere spaces. These invariants resemble t…
Oriented robot motion planning in Riemannian manifolds
Stephan Mescher
We consider the problem of robot motion planning in an oriented Riemannian manifold as a topological motion planning problem in its oriented frame bundle. For this purpose, we stud…
Perturbed gradient flow trees and -algebra structures on Morse cochain complexes
Stephan Mescher
We elaborate on an idea of M. Abouzaid of equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an -algebra.…