Topological complexity of real Grassmannians

Topological complexity of real Grassmannians

We use some detailed knowledge of the cohomology ring of real Grassmann manifolds Gk(ℝn) to compute zero-divisor cup-length and estimate topological complexity of motion planning for k-linear subspaces in ℝn. In addition, we obtain results about monotonicity of Lusternik–Schnirelmann category and to...

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Veröffentlicht in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2021-12, Vol.151 (6), p.2013-2029
1. Verfasser: Pavešić, Petar
Format: Artikel
Sprache:eng
Schlagworte:
Complexity
Estimates
Homology
Manifolds (mathematics)
Motion planning
Planning
Robotics
Subspaces
Topology
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Zusammenfassung:We use some detailed knowledge of the cohomology ring of real Grassmann manifolds Gk(ℝn) to compute zero-divisor cup-length and estimate topological complexity of motion planning for k-linear subspaces in ℝn. In addition, we obtain results about monotonicity of Lusternik–Schnirelmann category and topological complexity of Gk(ℝn) as a function of n.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2020.92