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pro vyhledávání: '"Mescher, Stephan"'
The Lusternik-Schnirelmann category of a space was introduced to obtain a lower bound on the number of critical points of a $C^1$-function on a given manifold. Related to Lusternik-Schnirelmann category and motivated by topological robotics, the topo
Externí odkaz:
http://arxiv.org/abs/2411.01980
Autor:
Mescher, Stephan
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 robots. The purpose of this survey is threefold. Firstly, we present a
Externí odkaz:
http://arxiv.org/abs/2402.07265
We generalize results from topological robotics on the topological complexity (TC) of aspherical spaces to sectional categories of fibrations inducing subgroup inclusions on the level of fundamental groups. In doing so, we establish new lower bounds
Externí odkaz:
http://arxiv.org/abs/2312.01124
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 cut loci over whose components the tangent cut loci fiber in a convenie
Externí odkaz:
http://arxiv.org/abs/2206.07691
Publikováno v:
Algebr. Geom. Topol. 23 (2023) 2221-2270
We study the geodesic motion planning problem for complete Riemannian manifolds and investigate their geodesic complexity, an integer-valued isometry invariant introduced by D. Recio-Mitter. Using methods from Riemannian geometry, we establish new lo
Externí odkaz:
http://arxiv.org/abs/2105.09215
Autor:
Mescher, Stephan
Publikováno v:
Calc. Var. 59, 155 (2020)
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 main tool in the proofs are spherical complexities, which have been intro
Externí odkaz:
http://arxiv.org/abs/2003.07259
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Autor:
Mescher, Stephan
Publikováno v:
Algebr. Geom. Topol. 21 (2021) 1021-1074
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 the Lusternik-Schnirelmann category and provide lower bounds for the nu
Externí odkaz:
http://arxiv.org/abs/1911.03948
Autor:
Mescher, Stephan
Publikováno v:
Topology Appl. 258 (2019), 1-20
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 study the topological complexity of oriented frame bundles, derive an uppe
Externí odkaz:
http://arxiv.org/abs/1810.06281