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Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Topological complexity of real Grassmannians
Part of
- Classical Topics in Algebraic Topology
- Operations and obstructions
Petar Pavešić
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 6 / December 2021

Published online by Cambridge University Press:

12 January 2021, pp. 2013-2029

Print publication:

December 2021
- Article
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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.