6 citations · 21 across the 10 of their papers we have counts for
13 papers
On open covers of aspherical spaces satisfying -constraints and bounded Adamson cohomology
Arturo Espinosa Baro, Stephan Mescher
Given a topological space and a family of subgroups of , the -category of is given as one less than the cardinality of the smallest cover…
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…
Sequential topological complexity of aspherical spaces and sectional categories of subgroup inclusions
Arturo Espinosa Baro, Michael Farber, Stephan Mescher +1
We generalize results from topological robotics on the topological complexity (TC) of aspherical spaces to sectional categories of fibrations inducing subgroup inclusions on the le…
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…
Existence results for closed Finsler geodesics via spherical complexities
Stephan Mescher
We apply topological methods and a Lusternik-Schnirelmann-type approach to prove existence results for closed geodesics of Finsler metrics on spheres and projective spaces. The mai…
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…
Topological complexity of symplectic manifolds
Mark Grant, Stephan Mescher
We prove that the topological complexity of every symplectically atoroidal manifold is equal to twice its dimension. This is the analogue for topological complexity of a result of…
On the topological complexity of aspherical spaces
Michael Farber, Stephan Mescher
The well-known theorem of Eilenberg and Ganea expresses the Lusternik - Schnirelmann category of an aspherical space as the cohomological dimension of its fundamental group. In thi…
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.…
A primer on A-infinity-algebras and their Hochschild homology
Stephan Mescher
We present an elementary and self-contained construction of -algebras, -bimodules and their Hochschild homology and cohomology groups. In addition, we discuss t…